Blowing up boundary conditions for a nonlocal nonlinear diffusion equation in several space dimensions

Abstract

We analyze boundary value problems prescribing Dirichlet or Neumann boundary conditions for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation in a bounded smooth domain Ω ∈ R N with N ≥ 1 . First, we prove existence and uniqueness of solutions and the validity of a comparison principle for these problems. Next, we impose boundary data that blow up in finite time and study the behavior of the solutions.