A Nonlinear Hyperbolic Volterra Equation in Viscoelasticity.

Abstract

A general model for the nonlinear motion of a one dimensional, finite, homogeneous, viscoelastic body is developed and analysed by an energy method. It is shown that under physically reasonable conditions the nonlinear boundary, initial value problem has a unique, smooth solution (global in time), provided the given data are sufficiently 'small' and smooth, moreover, the solution and its derivatives of first and second order decay to zero as t yields infinity. Various modifications and generalizations, including two and three dimensional problems, are also discussed.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1980
Accession Number
ADA089668

Entities

People

  • C. M. Dafermos
  • J. A. Nohel

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Constitutive Equations
  • Differential Equations
  • Displacement
  • Equations
  • Frequency Domain
  • Hilbert Space
  • Inequalities
  • Integrals
  • Mathematics
  • Partial Differential Equations
  • Three Dimensional
  • United States
  • Viscoelasticity
  • Viscosity
  • Volterra Equations
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms