Accession Number:

AD0707761

Title:

DIFFERENTIAL EQUATIONS ON CONVEX SETS,

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV LOS ANGELES NUMERICAL ANALYSIS RESEARCH

Personal Author(s):

Report Date:

1970-01-01

Pagination or Media Count:

24.0

Abstract:

Recent developments in the theory of semi-groups of non-linear transformations in Banach or Hilbert spaces have sharply brought into focus the fact that these theories must be developed for semi-groups on convex sets in order to achieve their full scope. The purpose of this note is to establish existence of solutions of a Cauchy problem of the form dudt gu,t, uO x, where the function g is only defined on a set of the form C X O,a for some convex set C in a Banach space. The methods used are not new, but the main result seems to have gone unnoticed and serves to clarify some of the theory of semi-groups of nonlinear transformations and the related theory of accretive mappings in Banach spaces. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE