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Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior. (English) Zbl 0836.35090
Summary: Existence and uniqueness is proved, in the class of functions satisfying a wave entropy condition, of weak solutions to a conservation law with a flux function that may depend discontinuously on the space variable. The large time limit is then studied, and explicit formulas for this limit are given in the case where the initial data as well as the \(x\) dependency of the flux vary periodically. Throughout the paper, front tracking is used as a method of analysis. A numerical example which illustrates the results and method of proof is also presented.

MSC:
35L65 Hyperbolic conservation laws
35R05 PDEs with low regular coefficients and/or low regular data
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
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