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

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.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1995
Accession Number
ADA304627

Entities

People

  • Athanasios E. Tzavaras

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Asymptotic Series
  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Differential Equations
  • Discontinuities
  • Eigenvalues
  • Equations
  • Functional Analysis
  • Military Research
  • Oscillation
  • Sequences
  • Shock Waves
  • Stress Strain Relations
  • Traveling Waves
  • Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.