
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 semigroups of nonlinear transformations in Banach or Hilbert spaces have sharply brought into focus the fact that these theories must be developed for semigroups 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 semigroups 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