Convergence of Difference Approximations of Quasilinear Evolution Equations.

Abstract

The very successful theory of quasilinear evolution equations, which applies to many problems of mathematical physics, has been developed by T. Kato. The theory obtains solutions of quasilinear problems via contraction mappings which are defined by means of a theory of linear evolution equations also developed by Kato. In the current work we show how the existence and continuous dependence theorems obtained by Kato can be proved by discretization in time. As opposed to earlier work in this direction, the current results are much sharper concerning the continuity properties of the solutions of the discretized problem and the strength of the norms in which they converge.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1984
Accession Number
ADA144694

Entities

People

  • M. G. Crandall
  • Panagiotis E. Souganidis

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Banach Space
  • Boundary Value Problems
  • Cauchy Problem
  • Differential Equations
  • Equations
  • Functional Analysis
  • Inequalities
  • Mathematics
  • Military Research
  • North Carolina
  • Numbers
  • Partial Differential Equations
  • Security
  • Standards
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.