Homogenization for a Volterra Equation.

Abstract

Nonlinear heat flow in a heterogeneous material is considered. In this model, the internal genergy and heat flux depend upon the history of the temperature and the gradient of the temperature respectively. The heat conservation law leads to a Nonlinear Volterra integrodifferential equation with appropriate boundary conditions. This problem is solved under physically reasonable assumptions and its homogenization is investigated: introducing a small parameter beta measuring the 'tightness' of the heterogeneity of the medium (typically we assume beta-periodicity for the physical parameters), the stability of the model is studied (as beta goes to zero) and the homogenized (ideal) limit medium is characterized in some cases, including the linear one. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1983
Accession Number
ADA134427

Entities

People

  • Alain Damlamian
  • Hedy Attouch

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Boundaries
  • Classification
  • Differential Equations
  • Equations
  • Heat Flux
  • Heat Transmission
  • Integral Equations
  • Materials
  • Mathematics
  • Military Research
  • North Carolina
  • Standards
  • Topology
  • United States
  • Volterra Equations
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Combustion and Flow Dynamics.