Abstract
In this paper we study a simple non-local semilinear parabolic equation in a bounded domain with Neumann boundary conditions. We obtain a global existence result for initial data whose L∞-norm is less than a constant depending explicitly on the geometry of the domain. A natural energy is associated to the equation and we establish a relationship between the finite-time blow up of solutions and the negativity of their energy. The proof of this result is based on a Gamma-convergence technique.
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