Energy and pointwise bounds in some non-standard parabolic problems

We study a class of initial-boundary-value problems for which an auxiliary condition of the form is prescribed. We determine bounds on an energy expression by means of differential inequalities and derive pointwise bounds for the solution and its gradient by use of a parabolic maximum principle.

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Bibliographic Details
Published inProceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 134; no. 1; pp. 1 - 9
Main Authors Ames, K. A., Payne, L. E., Schaefer, P. W.
Format Journal Article
LanguageEnglish
Published Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.02.2004
Cambridge University Press
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Summary:We study a class of initial-boundary-value problems for which an auxiliary condition of the form is prescribed. We determine bounds on an energy expression by means of differential inequalities and derive pointwise bounds for the solution and its gradient by use of a parabolic maximum principle.
Bibliography:PII:S0308210500003036
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content type line 23
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210500003036