Development of Singularities in Nonlinear Viscoelasticity

Abstract

This paper discusses the motion of nonlinear viscoelastic materials with fading memory in one space dimension. It concentrates on viscoelastic solids and briefly remark on similar results for fluids. After formulating the mathematical problems, the authors survey results for global existence of classical solutions to the initial value problem, provided the initial data are sufficiently small. They then discuss in some detail the development of singularities in initially smooth solutions for large data. Keywords: nonlinear hyperbolic problems; Volterra integrodifferential equations; dissipation; decay; shocks; viscoelastic fluids.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1985
Accession Number
ADA158190

Entities

People

  • J. A. Nohel
  • Michael Renardy

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Cauchy Problem
  • Coefficients
  • Contracts
  • Differential Equations
  • Dissipation
  • Equations
  • Formulas (Mathematics)
  • Inequalities
  • Intervals
  • Materials
  • Mathematics
  • Partial Differential Equations
  • United States
  • Viscoelasticity
  • Volterra Equations
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space
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