Accession Number : AD0707761

Title :   DIFFERENTIAL EQUATIONS ON CONVEX SETS,

Corporate Author : CALIFORNIA UNIV LOS ANGELES NUMERICAL ANALYSIS RESEARCH

Personal Author(s) : Crandall,Michael G.

Report Date : 1970

Pagination or Media Count : 24

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 du/dt = g(u,t), u(O) = 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)

Descriptors :   (*MAPPING(TRANSFORMATIONS), BANACH SPACE), (*GROUPS(MATHEMATICS), CONVEX SETS), (*CAUCHY PROBLEM, NUMERICAL INTEGRATION), TRANSFORMATIONS(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE