Product integral representation of time dependent nonlinear evolution equations in Banach spaces

Glenn Francis Webb

Vol. 32 (1970), No. 1, 269–281

DOI: 10.2140/pjm.1970.32.269

Abstract

The object of this paper is to use the method of product integration to treat the time dependent evolution equation u′(t) = A(t)(u(t)),t ≧ 0, where u is a function from [0,∞) to a Banach space S and A is a function from [0,∞) to the set of mappings (possibly nonlinear) on S. The basic requirements made on A are that for each t ≧ 0A(t) is the infinitesimal generator of a semi-group of nonlinear nonexpansive transformations on S and a continuity condition on A(t) as a function of t.

Mathematical Subject Classification

Primary: 47.80

Milestones

Received: 16 May 1969

Published: 1 January 1970