Date: 29 Sep 2006

A viscosity approximation to a system of conservation laws with no classical Riemann solution

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There are examples of systems of conservation laws which are strictly hyperbolic and genuinely nonlinear but for which the Riemann problem can be solved only for states which are sufficiently close together. For one such example, we introduce a particular type of artificial viscosity and show how it suggests a possible definition of "generalized" solution to the Riemann problem.