Accession Number : ADA304627

Title :   Wave Interactions and Variation Estimates For Self-Similar Viscous Limits in Systems of Conservation Laws.

Descriptive Note : Technical rept.,

Corporate Author : WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES

Personal Author(s) : Tzavaras, Athanasios E.

PDF Url : ADA304627

Report Date : FEB 1995

Pagination or Media Count : 66

Abstract : We consider the problem of self similar viscous limits for general systems of conservation laws. First, we give conditions so that the resulting boundary value problem admits solutions. In particular this covers the class of symmetric hyperbolic systems. Second, we show that if the system is strictly hyperbolic and the Riemann data are sufficiently close then the resulting family of solutions is of uniformly bounded variation and oscillation. Third, we construct solutions of the Riemann problem via self similar viscous limits and study the structure of the emerging solution and the relation of self similar viscous limits and shock profiles. The emerging solution consists of N wave fans separated by constant states. Each wave fan is associated with one of the characteristic fields and consists of a rarefaction, a shock, or an alternating sequence of shocks and rarefactions so that each shock adjacent to a rarefaction on one side is a contact discontinuity on that side.

Descriptors :   *SHOCK(MECHANICS), *MATHEMATICAL ANALYSIS, INTERACTIONS, LIMITATIONS, BOUNDARY VALUE PROBLEMS, SYMMETRY, PARTIAL DIFFERENTIAL EQUATIONS, CONSERVATION, DISCONTINUITIES, OSCILLATION, VISCOSITY, RAREFACTION.

Subject Categories : Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE