Spaces of weighted measures for conservation laws with singular shock solutions. (English) Zbl 0821.35096

Summary: We study a model system of two strictly hyperbolic conservation laws which is genuinely nonlinear but for which the Riemann problem has no global solution. Singular solutions are defined by means of a generalized Rankine-Hugoniot relation and an overcompressive condition on the discontinuity. We show that approximate solutions which can be constructed by several standard methods converge in a weighted measure space and that the error in the approximation converges to zero. Viscous approximations satisfy approximate entropy inequalities which imply the overcompressive condition.


35L65 Hyperbolic conservation laws
76L05 Shock waves and blast waves in fluid mechanics
35L67 Shocks and singularities for hyperbolic equations
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