Vol. 32, No. 1, 1970

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

Glenn Francis Webb

Vol. 32 (1970), No. 1, 269–281

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
Received: 16 May 1969
Published: 1 January 1970
Glenn Francis Webb
Department of Mathematics
Vanderbilt University
1326 Stevenson Center
Nashville TN 37240
United States