Donato, Andrea and Fusco, Domenico (2000) Wave features and infinitesimal group analysis for a second order quasilinear equation in conservative form. Memorie scientifiche di Andrea Donato, LXXVII. pp. 295-304.
In 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.
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