Nonlinear Viscoelastic Materials with Fading Memory.

Abstract

The equations governing the motion of viscoelastic materials with fading memory incorporate a nonlinear elastic-type response with a natural dissipative mechanical. Our purpose is to discuss the subtle effects of this mechanism in viscoelastic materials of Boltzmann type. Recent results on the global existence and decay of classical solutions for smooth and small data (in one space dimension) are reviewed for smooth and singular memory kernels; for smooth kernels a number of such results can be generalized to several space dimensions. A recent result on the development of singularities in finite time for large data is discussed; several open problems are formulated. A program for studying weak solutions for such systems, including the development of numerical algorithms, is outlined. Keywords: hyperbolic equations; Volterra equations.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1986
Accession Number
ADA172587

Entities

People

  • John A. Nohel

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Value Problems
  • Cauchy Problem
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Flow
  • Fluid Flow
  • Formulas (Mathematics)
  • Materials
  • Mathematical Models
  • Mathematics
  • Models
  • Partial Differential Equations
  • Universities
  • Volterra Equations
  • Wave Equations

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space