Nonlinear Volterra Equations for Heat Flow in Materials with Memory.

Abstract

Consider the nonlinear Volterra equation u(t) + (b*Au) not an element of f(t). This paper discusses existing and recent results for the following problems concerning this equation the global existence and uniqueness of solutions and their continuous dependence on the data; the boundedness and asymptotic behavior as t approaches infinity in th special cases when X = H is a real Hilbert space and A is either a maximal monotone operator on H or A is a subdifferential of a proper, convex, lower semicontinuous function; and the existence, boundedness, and asymptotic behavior of positive solutions in the general settting. The theory is used to study one possible model problem for heat flow in a material with 'memory' which can be transformed to the equivalent from of the equation under physically reasonable assumptions; the latter provide a motivation for the natural setting of much of the theory developed here.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1980
Accession Number
ADA089634

Entities

People

  • John A. Nohel

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Dead Reckoning
  • Differential Equations
  • Equations
  • Frequency
  • Frequency Domain
  • Functional Analysis
  • Heat Flux
  • Hilbert Space
  • Integral Equations
  • Mathematics
  • Partial Differential Equations
  • Two Dimensional
  • United States
  • Volterra Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space