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Invariant regions for systems of conservation laws. (English) Zbl 0535.35056
Necessary and sufficient conditions are given for a region in \({\mathbb{R}}^ n\) to be invariant for (Glimm) solutions of the system of n conservation laws \(u_ t+f(u)_ x=0.\) A number of examples are given, and some observation are made about the invariance of such regions for certain finite difference approximations of solutions of systems of conservation laws.

MSC:
35L65 Hyperbolic conservation laws
35B40 Asymptotic behavior of solutions to PDEs
35L40 First-order hyperbolic systems
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
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