The Blow-Up Behavior of the Heat Equation with Neumann Boundary Conditions

We establish the blow-up rate for the solution of the heat equation u t = u xx , 0 < x < 1, t > 0 subject to Neumann boundary conditions: u x (0, t) = 0, u x (1, t) = e u(1, t) with convex initial data.

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 188; no. 2; pp. 641 - 650
Main Author Deng, K.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.12.1994
Elsevier
Subjects
Exact sciences and technology
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Solution blow up
Neumann problem
Heat equation
Partial differential equation
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ISSN0022-247X
1096-0813
DOI10.1006/jmaa.1994.1450

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Summary:We establish the blow-up rate for the solution of the heat equation u t = u xx , 0 < x < 1, t > 0 subject to Neumann boundary conditions: u x (0, t) = 0, u x (1, t) = e u(1, t) with convex initial data.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1994.1450