A Remark on Semilinear Perturbations of Abstract Parabolic Equations.

Abstract

Abstract results are given which apply to semilinear parabolic equations. Simple examples are provided by initial-value problems for semilinear equation like u sub t = delta u + f(u). As applied to this situation, the results show that for suitable f and t greater than 0 the solution u(t,phi) of the problem with the initial-value phi varies continuously together with its space derivatives as phi varied in a weaker sense - e.g. small perturbations of phi in some L sub P-norms cause small changes in u(t,phi) in the space on continuously differentiable functions. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1984
Accession Number
ADA141695

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  • M. G. Crandall

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  • University of Wisconsin–Madison

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  • Energy and Power Technologies
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  • Mathematics

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