Weak Solution Classes for Parabolic Integro-Differential Equations

Abstract

This paper studies a class of integro-differential equations that arises in some models for heat conduction in materials with memory or for the deformation of visco-elastic membranes. Some classes of constitutive assumptions are given that ensure the existence of weak solutions for these models; i.e., stress or heat flux are integrable fields over the reference configuration. The models are hybrids between damped nonlinear wave equations and perturbed heat equations, and mathematical techniques for these different problems are combined to establish existence results.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1982
Accession Number
ADA120993

Entities

People

  • Hans Engler
  • Stephan Luckhaus

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Contracts
  • Curvature
  • Differential Equations
  • Electrical Solitons
  • Equations
  • Heat Flux
  • Materials
  • Mathematics
  • Membranes
  • New York
  • United States
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mechanical Engineering/Mechanics of Materials.