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Hyperbolic conservation laws with stiff relaxation terms and entropy. (English) Zbl 0806.35112
Summary: We study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms. Reduced systems, inviscid and viscous local conservation laws, and weakly nonlinear limits are derived through asymptotic expansions. An entropy condition is introduced for \(N \times N\) systems that ensures the hyperbolicity of the reduced inviscid system. The resulting characteristic speeds are shown to be interlaced with those of the original system. Moreover, the first correction to the reduced system is shown to be dissipative. A partial converse is proved for \(2 \times 2\) systems. This structure is then applied to study the convergence to the reduced dynamics for the \(2 \times 2\) case.

MSC:
35L65 Hyperbolic conservation laws
35B40 Asymptotic behavior of solutions to PDEs
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