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

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

2007-01-26

arxiv.org/abs/math/0701774v1

Annales de l'Institut Henri Poincar\'{e} Analyse non lin\'{e}aire 24 (2007) 17--39

Mathematics

Analysis of PDEs

Scientific paper

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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