Some Problems in Nonlinear Analysis

Abstract

A program for obtaining the basic results of Kato's theory of quasilinear evolution equations was obtained by the simpler methods of nonlinear semigroup theory (implicit differencing in time). Certain classes of parabolic and Hamilton-Jacobi equations show the existence and uniqueness of solutions if initial boundary value problems with singular (e.g., identically infinite) initial data and the continuous dependence of these singular solutions as the diffusion coefficient tends to zero. This work shows how certain pde questions motivated by the theory of large deviations can be treated in greater generality and provides a certain abstract framework for this as well as concrete estimates.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1989
Accession Number
ADA209991

Entities

People

  • Michael G. Crandall

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Availability
  • Boundaries
  • Boundary Value Problems
  • Classification
  • Coefficients
  • Differential Equations
  • Diffusion Coefficient
  • Dynamic Programming
  • Equations
  • Partial Differential Equations
  • Personal Information Managers
  • Phase Transformations
  • Point Theorem
  • Theses
  • Viscosity
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)