Accession Number:

AD0412786

Title:

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

Descriptive Note:

Corporate Author:

WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

• Fleming,Wendell H.

Report Date:

1963-06-01

Pagination or Media Count:

51.0

Abstract:

The Cauchy problem is considered for quasi linear parabolic partial differential equations of the type Lu Fs,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

Descriptors:

• *STOCHASTIC PROCESSES
• *OPERATORS(MATHEMATICS)
• GAME THEORY
• TAYLORS SERIES
• DIFFUSION
• MEASURE THEORY
• INEQUALITIES
• PARTIAL DIFFERENTIAL EQUATIONS
• PROBABILITY

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE