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Stability of a relaxation model with a nonconvex flux. (English) Zbl 0961.35017

The authors prove the existence of a travelling wave solution of the conservation laws equations with shock profile for a nonconvex flux, if its speed is subcharacteritic. The main purpose of the paper is to prove the stability of such a wave and to justify the relaxation schemes introduced in the paper of T. P. Liu [Commun. Math. Phys. 108, 153-175 (1987; Zbl 0633.35049)], for a nonconvex flux under the assumption, that the Rankine-Hugoniot and entropy conditions are satisfied.

MSC:

35B35 Stability in context of PDEs
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations

Citations:

Zbl 0633.35049
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