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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00126955
Contributor : Ahmad El Soufi <>
Submitted on : Friday, January 26, 2007 - 4:39:21 PM
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Ahmad El Soufi, Mustapha Jazar, Régis Monneau. A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2007, 24, pp.17--39. ⟨hal-00126955⟩

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