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
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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