Probabilistic Analysis of Semilinear Partial Differential Equations

Abstract

A major thrust of the original proposal was to find new probabilistic methods for dealing with semilinear partial differential equations. Mathematicians are currently devoting more of their attention to studying nonlinear partial differential equations since they recognize that descriptions of physical phenomena must incorporate nonlinear behavior. The author succeeded in finding a method for solving systems of semilinear elliptic equations by a new procedure which does not need the old hypotheses of quasi-monotone systems. It combines probability, analysis and a transfinite induction scheme to solve equations of a certain on a domain E in R sub d subject to boundary conditions u sub 1 = u sub 2 = ... u sub n 0 on the boundary of E.

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Document Details

Document Type
Technical Report
Publication Date
May 28, 1989
Accession Number
ADA209903

Entities

People

  • Joseph Glover
  • Kai L. Chung

Organizations

  • University of Florida

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Boundaries
  • Boundary Value Problems
  • Classification
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Integral Equations
  • Markov Processes
  • Mathematical Analysis
  • Mathematics
  • Oscillation
  • Partial Differential Equations
  • Potential Theory
  • Probability
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Theoretical Analysis.