Elastic as Limit of Viscoelastic Response, in a Context of Self-Similar Viscous Limits

Athanasios Tzavaras*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We study the equations of one-dimensional isothermal elastic response as the small viscosity limit of the equations of viscoelasticity, in a context of self-similar viscous limits for Riemann data. No size restrictions on the data or genuine-nonlinearity assumptions are imposed. The limiting procedure is justified and a solution of the Riemann problem for the equations of elasticity is obtained. The emerging solution is composed of two wave fans, each consisting of rarefactions, shocks and contact discontinuities, separated by constant states. At shocks the self-similar viscous solution has the internal structure of traveling waves, and an admissibility criterion identified by Wendroff [W] is fullfilled.

Original languageEnglish (US)
Pages (from-to)305-341
Number of pages37
JournalJournal of Differential Equations
Volume123
Issue number1
DOIs
StatePublished - Nov 20 1995

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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