The Cauchy Problem in One-Dimensional Nonlinear Viscoelasticity.

Abstract

The authors study the initial value problem for a nonlinear hyperbolic Volterra equation which models the motion of an unbounded viscoelastic bar. Under physically motivated assumptions, we establish the existence of a unique, globally defined, classical solution provided the initial data are sufficiently smooth and small. They also discuss boundedness and asymptotic behavior. Their analysis is based on energy estimates in conjunction with properties of strongly positive definite kernels. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1984
Accession Number
ADA141507

Entities

People

  • J. A. Nohel
  • W. J. Hrusa

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Cauchy Problem
  • Computations
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Inequalities
  • Integral Equations
  • Integrals
  • Materials
  • Mathematics
  • Partial Differential Equations
  • United States
  • Viscoelasticity
  • Volterra Equations
  • Wave Equations
  • Waves

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Mathematical Modeling and Probability Theory.
  • Statistical inference.