Date: 29 Sep 2006

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

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Abstract

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.

Research supported in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 86-0088, and by a grant from the Energy Laboratory, University of Houston. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.