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where Ω is a bounded domain in R with smooth boundary ∂Ω, J ∗ u(x, t) = ∫ RN J(x − y)u(y, t)dy, J: R −→ R is nonnegative, symmetric (J(z) = J(−z)), bounded and ∫ RN J(z)dz = 1, f(s) is positive, increasing, convex function for positive values of s and ∫ ∞ ds f(s) < ∞. The initial data u0 ∈ C1(Ω). We show that if ε is small enough, the solution of the above problem blows up in a finite time and its blow-up time goes to the one of the solution of the following differential equation

Blow-up time for a nonlocal diffusion problem with Dirichlet boundary conditions