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Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains

Laister, Robert; Robinson, James C.; Sierzega, Mikolaj

Authors

James C. Robinson

Mikolaj Sierzega



Abstract

We establish a local non-existence result for semilinear heat equations with Dirichlet boundary conditions and initial data in L^q when the source term f is non-decreasing. We construct a locally Lipschitz f satisfying the Osgood condition (which ensures global existence for bounded initial data), such that for every q there is an initial condition in L^q for which the corresponding semilinear problem has no local-in-time solution.

Journal Article Type Article
Publication Date Jan 1, 2014
Journal Comptes Rendus Mathematique
Print ISSN 1631-073X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 352
Issue 7-8
Pages 621-626
APA6 Citation equations of Osgood type in bounded domains. Comptes Rendus Mathématique, 352(7-8), 621-626. https://doi.org/10.1016/j.crma.2014.05.010
DOI https://doi.org/10.1016/j.crma.2014.05.010
Keywords local solutions, semilinear heat equations, Osgood, bounded domains
Publisher URL http://dx.doi.org/10.1016/j.crma.2014.05.010

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