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Titlebook: Nonlinear Hyperbolic Problems; Proceedings of an Ad Claude Carasso,Denis Serre,Pierre-Arnaud Raviart Conference proceedings 1987 Springer-V

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Two existence theorems for systems of conservation laws with dissipation,
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Global solutions to some free boundary problems for quasilinear hyperbolic systems and applications
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Computation of oscillatory solutions to partial differential equations, case for which the continous solution is not well resolved on the computational grid. Averaged difference approximations of linear problems and particle method approximations of semilinear problems are presented. Highly oscillatory solutions to the Carleman and Broadwell models are considered. The
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The entropy dissipation by numerical viscosity in nonlinear conservative difference schemes, viscosity present in such schemes, and relate it to their entropy stability by means of comparison. To this end, two main ingredients are used: the entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. We then show
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