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.

authors

Donaldson JA

doi

10.1073/pnas.68.9.2025

subject

Has Abstract

pub_date

1971-09-01 00:00:00

pages

2025-7

issue

9

eissn

0027-8424

issn

1091-6490

journal_volume

68

pub_type

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