An inverse problem for a semilinear parabolic equation

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1982 English Publisher:Springer Science and Business Media LLCJournal:Annali di Matematica Pura ed Applicata, volume 131, pages 145-166 (issn: 0373-3114, eissn: 1618-1891,

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Authors: Lorenzi, A.;

doi: 10.1007/bf01765150

An inverse problem for a semilinear parabolic equation

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Abstract

In this paper we are concerned with the study of the stability of an unknown non-linear term in a parabolic equation in dependence on over specified Cauchy-Dirichlet data prescribed on the parabolic boundary of the open set under consideration. Since, in general, the dependence of the nonlinear term upon the data is not stable with respect to L∞ -metrics, we show how a Holder continuity may be restored under mild restrictions for the set of admissible solutions.

Keywords

Inverse problems for PDEs, Nonlinear parabolic equations, semilinear parabolic equation, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Stability in context of PDEs, dependence upon over-determined Cauchy- Dirichlet data

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