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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.

MSC:

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