Lower bounds for blow-up time in parabolic problems under Neumann conditions

We consider an initial boundary value problem for the semilinear heat equation under homogeneous Neumann boundary conditions in which the solution may blow up in finite time. A lower bound for the blow-up time is determined by means of a differential inequality argument when blow up occurs. Under al...

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Bibliographic Details
Published inApplicable analysis Vol. 85; no. 10; pp. 1301 - 1311
Main Authors Payne, L. E., Schaefer, P. W.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.10.2006
Subjects
2000 Mathematics Subject Classifications: 35K05
Blow-up
Lower bounds
Parabolic problems
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ISSN0003-6811
1563-504X
DOI10.1080/00036810600915730

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Summary:We consider an initial boundary value problem for the semilinear heat equation under homogeneous Neumann boundary conditions in which the solution may blow up in finite time. A lower bound for the blow-up time is determined by means of a differential inequality argument when blow up occurs. Under alternative conditions on the nonlinearity, some additional bounds for blow-up time are also determined.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036810600915730