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arXiv:math/0701774 [math.AP]AbstractReferencesReviewsResources

A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions

Ahmad El Soufi, Mustapha Jazar, Régis Monneau

Published 2007-01-26Version 1

In this paper we study a simple non-local semilinear parabolic equation with Neumann boundary condition. We give local existence result and prove global existence for small initial data. A natural non increasing in time energy is associated to this equation. We prove that the solution blows up at finite time $T$ if and only if its energy is negative at some time before $T$. The proof of this result is based on a Gamma-convergence technique.

Journal: Annales de l'Institut Henri Poincar\'{e} Analyse non lin\'{e}aire 24 (2007) 17--39
Categories: math.AP
Subjects: 35B35, 35B40, 35K55
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