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Riemann problem for a \(2\times 2\) hyperbolic system with linear damping. (English) Zbl 1462.35196

Summary: In this paper, we study the Riemann problem for a \(2\times 2\) nonstrictly hyperbolic system with linear damping. We introduce the special time-dependent viscosity to obtain approximate solutions. Therefore, we solve the Riemann problem (1.1)-(1.2) by limiting viscosity approach.

MSC:

35L60 First-order nonlinear hyperbolic equations
35L67 Shocks and singularities for hyperbolic equations
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