Title: New Integral Representations for Solutions of Cauchy's Problem for Abstract Parabolic Equations
Abstract: A study has been made of Cauchy's problem for a class of abstract parabolic differential equations. Our study is based upon a transformation that maps solutions of second-order abstract Cauchy problems into solutions of first-order. This is a preliminary report on some of the results obtained. These results include ( 1 ) new representations for solutions of abstract parabolic equations, ( 2 ) applications to the heat equation, ( 3 ) a discussion of solution representations for second-order abstract Cauchy problems, and ( 4 ) applications to nonwell posed (in the sense of Hadamard) Cauchy problems.