Global Weakly Discontinuous Solutions to a Kind of Mixed Initial-boundary Value Problem for Inhomogeneous Quasilinear Hyperbolic Systems

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Abstract

In this paper we study the mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems in the domain D = {(t, x) | t ≥ 0, x ≥ 0}. Under the assumption that the source term satisfies the matching condition, a sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.

Keywords:

CInhomogeneous quasilinear hyperbolic system;mixed initial-boundary value problem;global weakly discontinuous solution;weak linear degeneracy;matching condition
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Global Weakly Discontinuous Solutions to a Kind of Mixed Initial-boundary Value Problem for Inhomogeneous Quasilinear Hyperbolic Systems. (2020). Journal of Partial Differential Equations, 20(4), 365-384. https://global-sci.com/index.php/jpde/article/view/4112