Messanae Universitas Studiorum: No conditions. Results ordered -Date Deposited. 2024-06-23T09:09:40ZEPrintshttps://cab.unime.it/images/sitelogo.pnghttp://cab.unime.it/mus/2005-09-26Z2012-09-14T11:21:12Zhttps://cab.unime.it/mus/id/eprint/332This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/3322005-09-26ZExceptionality condition and linearization of hyperbolic equationsAndrea DonatoFrancesco Oliveri2005-04-06Z2012-09-14T11:30:26Zhttps://cab.unime.it/mus/id/eprint/233This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/2332005-04-06ZA perturbation method for a point explosion model with small dissipationsWe consider the point explosion problem in a viscous, thermally conducting fluid and carry on an asymptotic analysis to take into account dissipative effects. The asymptotic waves propagating in a non constant state, characterized by a similarity solution are ruled by a generalized Burges equation with variables coefficents. This equation belong in the class of non-linear evolution equations considered in and the qualitative behaviour of the solution is pointed out.Andrea Donato2004-06-01Z2012-09-14T11:27:16Zhttps://cab.unime.it/mus/id/eprint/27This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/272004-06-01ZWave features related to a mathematical model describing pulse transmission in a nerve fibreIn order to describe the signal transmission in a nerve fibre, we consider a non-linear mathematical model which takes into account several dissipative mechanism. By assuming different orders of magnitude for the relaxtion times associated with each of them, we carry out an asymptotic analysis pointing out the wave features in different situationsAndrea DonatoDomenico Fusco2004-06-01Z2010-04-09T09:12:42Zhttps://cab.unime.it/mus/id/eprint/54This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/542004-06-01ZAn approach to Constrained Thermoelastic Solids:Internal Constraint responses and Wave propagationAndrea DonatoDomenico Fusco2004-06-01Z2010-04-13T09:38:09Zhttps://cab.unime.it/mus/id/eprint/69This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/692004-06-01ZOn the evolution of weak discontinuities in a state characterized by invariant solutionsA quasilinear hyperbolic system which has a constant state in appropriate similar variables. These constant state solutions become special non-constant state solutions in the original variables. Two physical examples from gas dynamics and elastic-plastic deformation are studied and the occurence of shock waves demonstratedAndrea DonatoW. F. Ames2004-06-01Z2012-09-14T11:22:19Zhttps://cab.unime.it/mus/id/eprint/82This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/822004-06-01ZWhen Nonautonomous Equations are Equivalent to Autonomous OnesWe consider nonlinear systems of first order partial differential equations admitting at least two one-parameter Lie groups of transformations with commuting infinitesimal operators. Under suitable conditions it is possible to introduce a variable transformation based on canonical variables which reduces the model in point to autonomous form. Remarkably, the transformed system may admit costant solutions to which three correspond non-costant solutions of the original model. The results are specialized to the case of first order quasilinear systems admitting either dilatation or spiral groups of transformations and a systematic procedure to characterize special exact solutions is given. At the end of the paper the equations of axi-symmetric gas dynamics are considered.Andrea DonatoFrancesco Oliveri2004-06-01Z2012-09-14T08:49:26Zhttps://cab.unime.it/mus/id/eprint/83This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/832004-06-01ZReduction to Autonomous Form by Group Analysis and Exact Solutions os Axisymmetric MHD EquationsMotivated by many physical applications, we consider a general first order system of nonlinear partial differential equations involving two independent variables x, t and a vector field u (x,t). We suppose that the system admits two one parameter Lie groups of transformations with commuting infinitesimal operators. Then, by introducing canonical variables, it is possible to show, under suitable conditions, that the original governing system may be written in autonomous form. Of course, constant solutions of the transformed system are nonconstant solutions of the original system. By using the above mentioned result, we are able to point out a systematic procedure that allows us to build up special nonconstant solutions provided that the governing system admits two commuting infinitesimal operators. The results obtained in [1], in the case when the system under consideration is invariant with respect to the stretching group of transformation can be recovered as a special case of our procedure. In dealing with waves propagating in media having cylindrical or spherical symmetry, as well as in regions with inhomogeneities, we are led, in the one-dimensional case, to consider hyperbolic systems where the independent variables appear explicity in the coefficients of the system. Consequently, it becomes a suitable procedure to transform the system in autonomous form characterizing, in the meantime, exact solutions. Moreover, it is possible to study discontinuity and shock waves propagating in such special nonconstant states as propagation problems in constant states of the transformed systemAndrea DonatoFrancesco Oliveri2004-06-01Z2010-04-13T09:38:15Zhttps://cab.unime.it/mus/id/eprint/95This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/952004-06-01ZPanchapagesan,T.V.";"On weakly compact operators onLet T be a locally compact Hausdorff space and let C0(T)= be provided with the supremum norm.Let X be a quasicomplete locally convex Hausdorff space.Suppose u : C0(T) -->X is a continuous linear operator.By refining the method adopted by Grothendick in [6] and by combining the integration technique of Bartle-Dunford-Schwartz [1],are obtained 32 characterizations for the operator u to be weakly compact,several of which are new.The present method is so powerful as to deduce the isolated result of Dinculeanu and Kluvanek on the regular Borel extension of o-additive locally convex space valued Baire measures as corollary of the main characterization theorem.Also is included an elegant proof of the range theorem of Tweddle on o-additive vector measures.Andrea Donato2004-06-01Z2012-09-14T11:25:04Zhttps://cab.unime.it/mus/id/eprint/62This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/622004-06-01ZOn the evolution of weak discontinuities in a state characterized by invariant solutionsA quasilinear hyperbolic system which has a constant state in appropriate similar variables. These constant state solutions become special non-constant state solutions in the original variables. Two physical examples from gas dynamics and elastic-plastic deformation are studied and the occurence of shock waves demonstratedAndrea DonatoW. F. Ames2004-06-01Z2012-09-14T11:22:41Zhttps://cab.unime.it/mus/id/eprint/81This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/812004-06-01ZApproximate Asymptotic SymmetriesWe modify the procedure of determining approximate one parameter group of transformations by introducing an asymptotic development which makes possible the matching between dissipative or dispersive effects and non-linearity. Once that the generators of the approximate group are determined approximate asymptotic invariant solutions can be determinedAndrea DonatoAnnunziata Palumbo2004-06-01Z2012-09-14T11:22:51Zhttps://cab.unime.it/mus/id/eprint/84This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/842004-06-01ZQuasilinear hyperbolic systems: Reduction to autonomous form and wave propagationWe consider quasilinear hyperbolic systems are left invariant by two Lie groups of transformations having commuting infinitesimal operators, it is shown how to reduce them to autonomous form. A physical example admitting two groups of transformations is considered; the application of the procedure allows us to characterize an exact particular solution. Finally, some considerations about the linearization of the model are pointed outAndrea DonatoFrancesco Oliveri2004-06-01Z2012-09-14T11:22:46Zhttps://cab.unime.it/mus/id/eprint/94This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/942004-06-01ZExceptionality Condition and Linearization Procedure for a Third Order Nonlinear PDEWe determine a third order hyperbolic nonlinear partial differential equation possessing the property of being completely exceptional ;i.e.,every admissible discontinuity wave never evolves into nonlinear shock wave.A special member of this class describes the Riemannian geometric theory of critical phenomena by requiring the scalar thermodynamic curvature to be proportional to the inverse of free energy.By using reciprocal transformations it is shown that certain subclasses may be reduced either to linear canonical forms or to an equation which is linear in the third order derivativesAndrea DonatoGiovanna Valenti2004-06-01Z2012-09-14T11:22:14Zhttps://cab.unime.it/mus/id/eprint/88This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/882004-06-01ZHow to build up variable transformation allowing one to mapo nonlinear hyperbolic equations into autonomous or linear onesThe paper claims to give a systematic approach allowing one to obtain invertible variable transformations mapping nonlinear partial differential equations either into autonomous or linear form provided that some suitable conditions are satisfed. The procedure makes use of Lie group analysis so that some symmetries are required in order to obtain the required transformations, which are related to canonical variables. A linearization procedure is given in the last part of the paper valid for systems of partial differential equations that can be reduced to a single nonlinear equation linearly degenerate. The procedures are explained with some examples of physical interest.Andrea DonatoFrancesco Oliveri2004-06-01Z2012-09-14T11:21:06Zhttps://cab.unime.it/mus/id/eprint/89This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/892004-06-01ZThe Monge-Ampere Equation and its Connection with Systems of Hydrodynamic TypeAndrea DonatoCarmela Curro'2004-06-01Z2012-09-14T11:21:03Zhttps://cab.unime.it/mus/id/eprint/91This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/912004-06-01ZWaves features related to a mathematical model of hypoplasticityWe consider model equations describing the two-dimensional deformation of an incompressible elastoplastic material with constitutive laws of rate type. By introducing suitable potentials, we are able to write the system in equivalent forms which are suitable in order to study the propagation of discontinuity waves. By requiring the system to be linear degenerate we are able to characterise a simple model with a special constitutive lawAndrea DonatoAnnunziata Palumbo2004-05-31Z2012-09-14T11:30:20Zhttps://cab.unime.it/mus/id/eprint/51This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/512004-05-31ZOn a supplementary conservation law for the energy equation in a rigid heat conductorAndrea Donato2004-05-31Z2012-09-14T11:27:21Zhttps://cab.unime.it/mus/id/eprint/55This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/552004-05-31ZOn a supplementary conservation law for the energy equation in a rigid heat conductorWe consider a rigid heat conductor with specified constitutive equations and show that the internal energy equation may be written in the form of a symmetric and conservative hyperbolic system of first order quasi-linear equations for wich the Cauchy problem is well-posed.Moreover,such a system is useful to study shocks.Several particular cases are examinedAndrea Donato2004-05-31Z2012-09-14T11:26:04Zhttps://cab.unime.it/mus/id/eprint/61This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/612004-05-31ZSimilarity analysis and non-linear wave propagationWe characterize the most general 2 x 2 first order quasilinear hyperbolic systems in conservative form which are invariant solutions satisfy,under suitable conditions,an autonomous first order system of ordinary differential equations.A procedure is given to characterize the profile of the velocities of the strong and weak discontinuities.Andrea Donato2004-05-31Z2012-09-14T11:25:40Zhttps://cab.unime.it/mus/id/eprint/66This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/662004-05-31ZAnalysis of the threadline equationsAndrea DonatoW. F. AmesM. C. Nucci2004-05-31Z2012-09-14T11:23:05Zhttps://cab.unime.it/mus/id/eprint/71This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/712004-05-31ZA Perturbation method for point explosion model with small dissipationsWe consider the point explosion problem in a viscous, thermally conducting fluid and carry on an asymptotic analysis to take into account dissipative effects.The asymptotic waves propaggating in a non costant state,characterized by a symilarity solution are ruled by a generalized Burges equation with variables coefficients.This equation belong in the class of non-linear evolution equations considered in [4] and the qualitative behaviour of the solutin is pointed outAndrea Donato2004-05-31Z2012-09-14T11:22:59Zhttps://cab.unime.it/mus/id/eprint/79This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/792004-05-31ZApproximate invariant solutions to dissipative systemsWe develop a procedure based on the concept of approximate symmetries to try for approximate invariant solutions to dissipative systemsAndrea DonatoAnnunziata Palumbo2004-05-31Z2012-09-14T11:31:16Zhttps://cab.unime.it/mus/id/eprint/43This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/432004-05-31ZThe occurence of singularties in solutions of homogeneous systems of two first order quasilinear hyperbolic equations with smooth initial dataAn unfolding procedure for an arbitrary initial curve in the hodograph plane is used to determine the influence of initial values on the breakdown of the solution to quasi-linear hyperbolic systems involving two first order homogeneous equations in one space dimension and time.The notion of addditively separable Riemann invariants is introduced and a general expression for the critical time at which breakdown occurs in systems with this property is obtained and then applied to several physical examples. Some important properties of a system that both reducible and strictly exceptional are also derived establishing its connection with the linear homogeneous wave equation.Andrea DonatoAlan Jeffrey2004-05-31Z2012-09-14T11:30:35Zhttps://cab.unime.it/mus/id/eprint/48This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/482004-05-31ZSome Applications of the Riemann Method to Electromagnetic Wave Propagation in Nonlinear MediaAndrea DonatoDomenico Fusco2004-05-31Z2012-09-14T11:25:30Zhttps://cab.unime.it/mus/id/eprint/64This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/642004-05-31ZOn nonlinear plane vibration of a moving threadlineAndrea DonatoFrancesco Oliveri2004-05-31Z2012-09-14T11:24:44Zhttps://cab.unime.it/mus/id/eprint/68This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/682004-05-31ZNonlinear waves propagating into a non-costant stateSummary.We characterize quasilinear dissipative systems invariant with respect to a stretching group of transformation.The propagation of asymptotic waves is studied in a non-costant state described by a similarity solution.Andrea DonatoCarmela Curro'2004-05-31Z2012-09-14T11:22:57Zhttps://cab.unime.it/mus/id/eprint/75This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/752004-05-31ZThe(3+1)-dimensional Monge-Ampere equation in discontinuity wave theory: application of a reciprocal transformationIt is shown that the completeexceptionality condition for discontinuity waves associated with a second-order non-linear hyperbolic equation of the form (..) leads to a Monge-Ampere-type equation in 3+1 dimensions.Application of a novel reciprocal trasformation shows that an important subclass may be reduced to linear canonical form.Specialization to 1+1 dimensions yields linearization of a Boillant-type equation satisfying the complete exceptionality criterior.In this last case the trasformation allowing the linearization coincide with the one introduced by Hoskinns and Bretherton in the theory of atmospheric frontogenesis and so-called geostrophic transformation.Finally,always in 1+1 dimensions,we show that the .... equation is also strictly exceptional,i.e.the only possible shocks are characteristic.Andrea DonatoUsha RamgulamColin Rogers2004-05-28Z2012-09-14T11:31:14Zhttps://cab.unime.it/mus/id/eprint/47This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/472004-05-28Zinfluence of a strong discontinuity on the propagation of second order discontinuities";"We study the propagation of second order weak discontinuities in quasi-linear hyperbolic system of equations with discontinuous coefficients. The general theory is applied to shallow water wavesAndrea Donato2004-05-28Z2012-09-14T11:30:28Zhttps://cab.unime.it/mus/id/eprint/49This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/492004-05-28ZSu alcune proprieta' di un modello matematico atto a descrivere fenomeni ereditari in un dielettrico non lineareSi propone un modello non lineare per lo studio della propagazione di onde elettromagnetiche nei dielettrici in presenza di fenomeni ereditari. si caratterizza, tra l'altro, la classe piAndrea DonatoDomenico Fusco2004-05-28Z2012-09-14T11:27:12Zhttps://cab.unime.it/mus/id/eprint/53This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/532004-05-28ZGroup analysis for a linear hyperbolic equation arising from a quasilinear reducible systemThe aim of this paper is to carry out infinitesimal group analysis for a second order hyperbolic equation in canonical form. To such a kind of equation one could be led in considering the hodograph transformation for a first order reducible system. In the first part of the paper we characterize the most general expression for the generator of the Lie group, which has an infinite dimensional algebra. Then we calculate the invariant surfaces in some special cases of interest, and point out the corresponding ordinary differential equations whose integration allows us to determine possible classes of solutions for the equation we are consideringAndrea Donato2004-05-28Z2012-09-14T11:27:18Zhttps://cab.unime.it/mus/id/eprint/56This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/562004-05-28ZOn a supplementary conservation law for the balance laws in thermoelastic bodiesSi caratterizza un solido termoelastico riguardando la seconda legge della termodinamica come una legge supplementare di conservazione compatibile con le equazioni del moto. Si ottengono delle condizioni sufficienti per l'iperbolicita' del sistema base che puo' essere posto in forma simmetrica e conservativa.Andrea Donato2004-05-28Z2012-09-14T11:25:57Zhttps://cab.unime.it/mus/id/eprint/59This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/592004-05-28ZWave features and infinitesimal group analysis for a second order quasilinear equation in conservative formIn this paper we consider a quasilinear second order equation in conservative form.The complete exceptionally condition is used as a vehicle for characterizing classes of constitutive laws by which a weak discontinuity wave cannot evolve into a non-linear shock. As these classes of response functions involve arbitrary functions of the dependent variable, the invariance condition is required further in order to determine completely the functional form of the constitute laws for the model of interest. The last part of the paper is concerned with relevant examples of second order equations arising from different physical frameworks for which the theory developed herein holds.Andrea DonatoDomenico Fusco2004-05-28Z2012-09-14T11:27:07Zhttps://cab.unime.it/mus/id/eprint/60This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/602004-05-28ZOnde eccezionali ed analisi gruppale per la caratterizzazione di legami costitutiviAndrea Donato2004-05-28Z2012-09-14T11:25:07Zhttps://cab.unime.it/mus/id/eprint/63This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/632004-05-28ZInstability condition for symmetric quasi linear hyperbolic systemIn this paper a procedure is given allowing to obtain instability condition for quasi linear hyperbolic system in conservative form which are compatible with a supplementary conservative law. An application of the method to the Euler equation deriving form a Lagrangian is also carried outAndrea DonatoFrancesco Oliveri2004-05-28Z2012-09-14T11:26:13Zhttps://cab.unime.it/mus/id/eprint/65This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/652004-05-28ZInvariant solutions and nonlinear wave propagationWe consider quasi-linear hyperbolic system in the one-dimensional case, which are invariant with respect to infinitesimal groups of trasformations and we study the propagation of weak discontinuities across a similarity line. We are led to suitable compatibility conditions which are certainly fulfilled in the case of invariance with respect tothe stretching group. The result are applied to the equation governing the deformations of an infinitive axi-symmetric elastic-plastic mediumAndrea Donato2004-05-28Z2012-09-14T11:24:32Zhttps://cab.unime.it/mus/id/eprint/67This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/672004-05-28ZLinearization procedure of nonlinear first order system of partial differential equations by means of canonical variables related to lie group of point trasformationsan algorithm is given to linearize nonlinear first order systems of partial differential equations admitting an infinite-parameter lie group of point trasformations. The associated infinitesimal operator must be a linear combination of commuting operators which individually are not necessarily admitted by the basic system, whereas the cofficents of the combination are given by arbitrary solutions of suitable linear system. The procedure is based on the introduction of the canonical variables corresponding to the commuting operators. Within such a framework we reformulate a theorem already proved by Kumei and Bluman [SIAM J. appl. math. 42 (1982)]. The paper concludes with some illustrative examples of the proposed algorithmAndrea DonatoFrancesco Oliveri2004-05-28Z2012-09-14T11:22:32Zhttps://cab.unime.it/mus/id/eprint/70This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/702004-05-28ZOn some first order systems reducible to monge-ampere equations and their linearizationWe consider systems of equations in one space dimension in conservative form which can be reduce, with the aid of suitable potentials, to second order or third order monge-ampere equations. Under special cirumstances these equations may be linearized by means of backlund type trasformations. Fluid-dynamic,magnetogasdynamic and continuum models with rate-type costitutive laws belong to these classes of linearizable systems when suitable conditions are satisfatedAndrea DonatoAnnunziata Palumbo2004-05-28Z2010-04-13T09:38:10Zhttps://cab.unime.it/mus/id/eprint/73This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/732004-05-28ZA quasilinear hyperbolic system which has a constant state in appropriate similar variables. These constant state solutions become special non-constant state solutions in the original variables. Two physical examples from gas dynamics and elastic-plastic deformation are studied and the occurence of shock waves demonstratedAndrea DonatoM. C. Nucci2004-05-28Z2012-09-14T11:22:54Zhttps://cab.unime.it/mus/id/eprint/74This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/742004-05-28ZPerturbation method for a generalized burger's equationA perturbation method based on the linear theory of operators [5] for solving non-linear problems is used ti find an approximate solution of a generalized burger's equations governing the shock structure in a viscous thermally conducting fluidAndrea DonatoCarmela Curro'A. Povzner2004-05-28Z2012-09-14T11:21:08Zhttps://cab.unime.it/mus/id/eprint/76This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/762004-05-28ZOn a possible model to explain phytoplankton blooms produced by a receding edgeWe present a mathematical model to describe the interaction of ice-ocean-plankton in the Southern Ocean, based on a similar model used for blooms in the estuaries. The model obtained is hyperbolic and wave phenomena may be studied. travelling wave solutions are related to the formations of blooms.Andrea DonatoGiovanna Valenti2004-05-28Z2013-01-22T11:41:28Zhttps://cab.unime.it/mus/id/eprint/46This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/462004-05-28ZSulla possibilita' di urti secondari in un flusso autosimilareWe study the propagation of weak discontinuities in order to determine the existence of secondary shocksAndrea DonatoGiuseppe Ricca2004-05-28Z2012-09-14T11:30:32Zhttps://cab.unime.it/mus/id/eprint/50This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/502004-05-28ZNon-linear wave propagation in a layered half spaceIn this paper we consider the one dimensional propagation of weak discontinuities through a layered half space where quasilinear hyperbolic systems in homogeneous conservative form are involved. The amplitude of reflected and transmitted discontinuities across each layer is determined in terms of the initial conditions. The critical time when the incident wave breaks down is discussed. The results are specialized in the case of periodic layering. Physical examples are considered at the end of the paper.Andrea DonatoDomenico Fusco2004-05-28Z2012-09-14T11:30:23Zhttps://cab.unime.it/mus/id/eprint/52This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/522004-05-28ZSu alcune proprieta' di un modello iperbolico per la propagazione del caloreIn this paper we consider the heat propagation hyperbolic model for a rigid conductor proposed in [1] by M. E. Gurtin and A. C. Pipkin. By means of a Legendre transformation of the field variables, the governing equations may be written in symmetric and conservative form. Moreover we point out some properties concerning with exceptionality conditions and shock waves. Among other things we are able to characterize some functional forms for the free energy by which a weak discontinuity wave never breaks down.Andrea DonatoDomenico Fusco2004-05-28Z2012-09-14T11:30:14Zhttps://cab.unime.it/mus/id/eprint/58This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/582004-05-28ZAn approach to constrained thermoelastic solids: internal constraint responses and wavve propagationThermomechanical restrictions on thermodynamic processes in a thermoelastic solid are studied within the thermodynamical framework proposed by I. miller. By means of suitable assumptions on the form of constraints responses is chracterized. Moreover the main features of wave propagation in constrained thermomechanical media are pointed outAndrea DonatoDomenico Fusco2004-05-28Z2012-09-14T11:22:29Zhttps://cab.unime.it/mus/id/eprint/72This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/722004-05-28ZHow to use canonical variables to linearize systems of partial differential equationsIn this paper it is shown an algorithm leading to linearization of nonlinear systems of partial differential equations admitting infinite-parameter lie groups of point trasformations. The linearization is carried out through the introduction of canonical variables. The canonical variables are privileged variables allowing to write a general lie group of point trasformations in its simplets form (a translation in only one variable). Various relevant examples of application of the procedure are consideredAndrea DonatoFrancesco Oliveri2004-05-28Z2012-09-14T11:21:01Zhttps://cab.unime.it/mus/id/eprint/77This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/772004-05-28ZSimilarity solutions and strong shocks in extended thermodynamics of rarefied gas.We consider the equations of a monoatomic gas, in the context of the extended thermodynamic theory, with spherical symmetry and we look for similarity solutions. The classical problem of the point explosion is considered in order to get some qualitative information due to the presence of the heat flux and the dissipation. It seems that, despite to the classical case, a sub-shock formation cannot be avoideAndrea DonatoTommaso Ruggeri2004-05-27Z2012-09-14T11:31:29Zhttps://cab.unime.it/mus/id/eprint/42This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/422004-05-27ZThe propagation of weak discontinuities in quasi-linear hyperbolic systems when a characteristic shock occursIn this paper we study the propagation of weak discontinuities in quasi-linear hyperbolic systems of equations with discontinuous coefficients when one or more speeds of propagation of the discontinuity wavw is coincident with the speed of propagation of the strong discontinuityAndrea Donato2004-05-27Z2012-09-14T11:31:18Zhttps://cab.unime.it/mus/id/eprint/45This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/452004-05-27ZSu una classe di equazioni conservative ed iperboliche completamente eccezionali e compatibili con una legge di conservazione supplementareWe characterize a set of second order hyperbolic conservative equations that are both compatible with a supplementary conservation law and completely exceptionalAndrea DonatoGiovanni Crupi2004-05-27Z2012-09-14T11:31:40Zhttps://cab.unime.it/mus/id/eprint/44This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/442004-05-27ZInfluence of a Strong Discontinuity on the Propagation of waves in a Ferromangeic Materialsi considera la propagazione di discontinuita' deboli in un mezzo non lineare (ferromagnatico o ferroeletrrico) in contatto con uno lineare. Si caratterizzano le onde riflesse e le onde trasmesse, mettendo in evidenza alcune propiieta di cui godono. I risultati vengono genaralizzati al caso in cui i materiali a contatto siano entrambi non lineari.Andrea DonatoDomenico Fusco2004-05-26Z2012-09-14T11:36:30Zhttps://cab.unime.it/mus/id/eprint/23This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/232004-05-26ZSulle onde d'urto in magneto-elasticita'The magneto-elastic shock waves propagations is studied and the eventual occurens of characteristic shock is investigated. Three propagation modes are founded which correspond to three different values of the propagation velocity and it is noticed that only one of the three shock waves is, in genera, characteristic. Finally, having stated some realtions among propagation velocities,the different behaviour of H2 across the three shock surfaces, associated with the transverse, slow and fast waves, is pointed outAndrea Donato2004-05-26Z2012-09-14T11:36:22Zhttps://cab.unime.it/mus/id/eprint/24This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/242004-05-26ZOn supplementary convesation laws for second order hyperbolic consevative equationIn questa nota si determina la classe delle equazioni conservative del secondo ordine di forma canonica che ammettono una equazione di conservazione supplementare, seguendo un procedimento dovuto a G.Boillat. Si ha occasione di illustrare il metodo su un esempio particolareAndrea Donato2004-05-26Z2012-09-14T11:37:14Zhttps://cab.unime.it/mus/id/eprint/25This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/252004-05-26ZSulla eccezionalita' delle onde di mutua influenza magneto-elasticaBy reducing magneto-elasticity waves study to a first order system it is shown that discontinuity waves of magneto-elastic mutually influence are exceptional. It is also pointed out that the second derivative of two of three possible propagation velocities, generally undergoes a discontinuity across the wave frontAndrea Donato2004-05-26Z2012-09-14T11:35:01Zhttps://cab.unime.it/mus/id/eprint/28This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/282004-05-26ZThe Burgers' Equation in Magneto-thermo-elasticity with One-dimensional DeformationAndrea Donato2004-05-26Z2012-09-14T11:33:02Zhttps://cab.unime.it/mus/id/eprint/31This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/312004-05-26ZLegge di conservazione supplementare per un particolare sistema iperbolico del primo ordineWe consider a hyperbolic system of first order obtained by reducing a conservative hyperbolic equation of second order in noncanonical form. We determine, generalizing a previous paper, the conditions for having a supplementary conservation law. As a particular case we obtain that teh second order equation must be of Euler type with the usual conservation law for the energy.Andrea Donato2004-05-26Z2012-09-14T11:22:26Zhttps://cab.unime.it/mus/id/eprint/34This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/342004-05-26ZReduction to autonomous form by means of canonical variablesIn this paper it is shown to transform to autonomous form a general nonautonomous system of partial differential equations in n independent variables provides it is left invariant by n Lie groups of point transformations generating a n-dimensional Abelian Lie algebra. Two examples of physical interest are given to illustrate how the algorithm worksAndrea DonatoFrancesco Oliveri2004-05-26Z2012-09-14T11:32:38Zhttps://cab.unime.it/mus/id/eprint/35This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/352004-05-26ZLegge di evoluzione delle discontinuita' e determinazione di una classe di pontenziali elastici compatibile con la propagazione di onde eccenzionali in un mezzo continuo sottoposto a particolori deformazioni finiteAndrea Donato2004-05-26Z2012-09-14T09:16:59Zhttps://cab.unime.it/mus/id/eprint/21This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/212004-05-26ZOnde di discontinuita' e condizioni di eccezionalita' per materiali ferromagneticiWe studied the propagation of first-order electromangetic discontinuites throught ferromagnetic materials whose magnetic permeabily is a fuction of h2. We examined the condition for a discontinuity -wawe no to generate a shock-wave (exceptionality conditons of lax-Boilant). We found thet the system is never fully exceptional, unless in the plane wave case , if one supposes Ht=0, or for Hn= 0 with materials whose magnetic permeabily solves , a suitable a differential equationAndrea DonatoTommaso Ruggeri2004-05-26Z2012-09-14T11:32:00Zhttps://cab.unime.it/mus/id/eprint/33This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/332004-05-26ZSulla propagazione di onde di discontinuita' compatibili con un modello magneto-elastico completamente non lineareI an earlier paper we deduced the magneto-elastic system of equations in the three-dimensional case. The object of the present paper is to study the propagation of weak discontinuities associated with the system. We have occasion to compare results with other ones known in absence of magnetic field. In the last part of the paper we examine the case of small deformations obtaining the same results as inAndrea DonatoDomenico Fusco2004-05-26Z2012-09-14T11:31:23Zhttps://cab.unime.it/mus/id/eprint/37This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/372004-05-26ZOn the influence of initial conditions on the motion of water confined within a tankThe aim of this paper is to investigate the influence of initial values on the motion of waves in shallow water confined between two vertical walls of a tank with a polygonal bottom. A method introduced by G.S.S Ludford to study a Riemann problem in gas dynamics is modified and used to obtain an estimate of the time of breakdown of an initially smooth but arbitrary wave motion on the surface of the waterAndrea DonatoAlan Jeffrey2004-05-26Z2012-09-14T11:30:17Zhttps://cab.unime.it/mus/id/eprint/26This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/262004-05-26ZGeneralized 'shock structure' in a non linear viscoelastic mediumFollowing a procedure given in we construct an asymptotic expansion which generalizes the classical shock structure solution in a non linear viscoelastic medium. The method can be used in order to get solutions, valid everywhere, also when a known shock line divides two different materials that are both viscoelastic or one in elastic and the other one viscoelasticAndrea DonatoG. Vermiglio2004-05-26Z2012-09-14T11:22:23Zhttps://cab.unime.it/mus/id/eprint/36This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/362004-05-26ZLinearization of Completely Exceptional Second Order Hyperbolic Conservative EquationsThe formation of nonlinear shocks does not occur for nonlinear hyperbolic partial differential equations which are 'completely exceptional'. In some sense the solutions of these equations exhibit a behaviour similar to that of linear equations. We present a procedure which allows to transform, under suitable conditions, such type of equations to linear canonical form. The procedure is valid for more than one space dimension and allows also to characterize classes of linearizable systemsAndrea DonatoFrancesco Oliveri2004-05-25Z2012-09-14T09:14:18Zhttps://cab.unime.it/mus/id/eprint/19This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/192004-05-25ZSu alcuni integrali primi nella dinamica relativistica del punto a massa variabileSi deducono alcune condizioni cinematiche e dinamiche che consentono l'esistenza di integrali primi del moto, nella dinamica relativistica del punto a massa variabileAndrea Donato2004-05-25Z2012-09-14T09:16:45Zhttps://cab.unime.it/mus/id/eprint/22This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/222004-05-25ZConsiderazioni sui campi elettromagnetici generalizzatiAndrea Donato2004-05-25Z2012-09-14T11:31:48Zhttps://cab.unime.it/mus/id/eprint/32This item is in the repository with the URL: https://cab.unime.it/mus/id/eprint/322004-05-25ZOn a magneto-elastic system with discontinuous coefficients and the propagation of a weak discontinuityIn questa nota si deduce un sistema di equazioni per la Magneto-elasticita' con deformazioni finite nel caso tridimensionale. Come applicazione si studia la propagazione di una discontinuita' debole nella ipotesi che i coefficienti delle equazioni risultano essi stessi discontinui. Tale ipotesi risulta verificata, ad es., quando si considerano due differenti mezzi magneto-elastici uno in contatto con l'altroAndrea Donato