A Simplified Proof of a Liouville Theorem for Nonnegative Solution of a Subcritical Semilinear Heat Equations

We give a new proof of the Liouville theorem proved by Merle and Zaag for nonnegative solutions of the semilinear heat equation with power nonlinearity. Our proof has a pedagogical interest and is based on Kaplan’s blow-up criterion.

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Bibliographic Details
Published inJournal of dynamics and differential equations Vol. 21; no. 1; pp. 127 - 132
Main Author Nouaili, Nejla
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.03.2009
Springer Verlag
Subjects
Analysis of PDEs
Applications of Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Heat equation
Liouville theorem
Kaplan’s criterion
35K05
35A20
35K55
Blow-up
Kaplan's criterion
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Summary:We give a new proof of the Liouville theorem proved by Merle and Zaag for nonnegative solutions of the semilinear heat equation with power nonlinearity. Our proof has a pedagogical interest and is based on Kaplan’s blow-up criterion.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-008-9121-6