Donato, Andrea and Jeffrey, Alan (2000) The occurence of singularties in solutions of homogeneous systems of two first order quasilinear hyperbolic equations with smooth initial data. Memorie scientifiche di Andrea Donato. pp. 127-134.
An 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.
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