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

摘要

This paper concerns the study of the following initial-boundary value problem where Q is a bounded domain in l" with smooth boundary dfl, J * u(x, t) = JRN J(X - y)u(y, t)dy, J: M.N -> M is nonnegative, symmetric (J(z) = J(-z)), bounded and fRN J(z)dz = 1, f(s) is positive, increasing, convex function for positive values of s and J°° -4^ < oo. The initial data uo ? C1(f2) We show that if e 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.