Initial Value Problems in Viscoelasticity

Abstract

This document reviews some recent mathematical results concerning integrodifferential equations that model the motion of one-dimensional nonlinear viscoelastic materials. In particular, the authors discuss global (in time) existence and long-time behavior of classical solutions, as well as the formation of singularities in finite time from smooth initial data. Although the mathematical theory is comparatively incomplete, some remarks are more concerning the existence of weak solutions (i.e., solutions with shocks). Some relevant results from linear wave propagation will also be discussed. Keywords: integrodifferential equations; mathematical models; Nonlinear viscoelasticity, materials with fading memory, viscoelastic fluids, linear wave propagation, acceleration waves, smooth kernels, singular kernels, Laplace transforms, hyperbolic equations, global existence, smooth solution.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1988
Accession Number
ADA196052

Entities

People

  • J. A. Nohel
  • Michael Renardy
  • W. J. Hrusa

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Applied Mathematics
  • Banach Space
  • Boundary Value Problems
  • Cauchy Problem
  • Constitutive Equations
  • Continuum Mechanics
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Linear Momentum
  • Materials
  • Mathematics
  • Modulus Of Elasticity
  • Partial Differential Equations
  • Volterra Equations
  • Wave Equations
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

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