A viscosity approximation to a system of conservation laws with no classical Riemann solution
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.
KeywordsHyperbolic System Riemann Problem Singular Solution Artificial Viscosity Riemann Solution
Unable to display preview. Download preview PDF.
- 5.B. L. Keyfitz and H. C. Kranzer, "A system of conservation laws with no classical Riemann solution," preprint (1988).Google Scholar
- 6.Ph. Le Floch, "Nonlinear hyperbolic systems under nonconservative form," to appear in Comm in PDE (1988).Google Scholar
- 7.P. D. Lax, "Shock waves and entropy," in Contributions to Nonlinear Functional Analysis, (ed Zarantonello), Academic Press, New York (1971), 603–634.Google Scholar
- 8.M. Slemrod, "A limiting ‘viscosity’ approach to the Riemann problem for materials exhibiting change of phase," Univ. of Wisconsin preprint (1987).Google Scholar