THE CAUCHY PROBLEM FOR DEGENERATE PARABOLIC EQUATIONS OF STOCHASTIC CONTROL THEORY,

Abstract

The Cauchy problem is considered for quasi linear parabolic partial differential equations of the type L(u) F(s,x,u,ux) 0. The matrix of coefficients of the second order terms uxixj in the second-order linear parabolic operator L is nonnegative definite, but not necessarily positive definite. Using a technique based on the theory of diffusion processes and game theory, a priori estimates for u and its gradient ux are obtained. Theorems about the existence of generalized solutions and their dependence of small parameters are then proved. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1963
Accession Number
AD0412786

Entities

People

  • Wendell H. Fleming

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Cauchy Problem
  • Coefficients
  • Control Theory
  • Differential Equations
  • Diffusion
  • Equations
  • Fokker Planck Equations
  • Game Theory
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Stochastic Control

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Fluid Dynamics.
  • Linear Algebra