The Riemann Problem for the System u(t) + Sigma(x) = O and (Sigma - f(u))(t) + (sigma - muf(u)) = o.

Abstract

In this paper we study the Riemann Problem for a system of conservation laws which exhibit internal friction similar to that seen in viscoelastic solids of the maxwell type. The solutions we obtain have a single shock and a single contact discontinuity and off of these singular curves they are smooth. The results we obtain are two fold. First we show this problem is globally solvable in time; this requires precise a-priori estimates for the solution off of the singular curves. Secondly, we obtain asymptotic or large time information about the solution which guarantees that in a weak sense it converges to special traveling wave solutions of the equations with compatible data. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1981
Accession Number
ADA110468

Entities

People

  • J. M. Greenberg
  • Ling Hsiao

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Cauchy Problem
  • Constitutive Equations
  • Differential Equations
  • Discontinuities
  • Equations
  • Equations Of Motion
  • Formulas (Mathematics)
  • Friction
  • Guarantees
  • Identities
  • Inequalities
  • Internal Friction
  • Mathematics
  • Partial Differential Equations
  • Shock
  • Shock Waves
  • Traveling Waves

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Calculus or Mathematical Analysis
  • Fluid Dynamics.