DIFFERENTIAL EQUATIONS ON CONVEX SETS,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1970
- Accession Number
- AD0707761
Entities
People
- Michael G. Crandall
Organizations
- University of California, Los Angeles