We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove ...

We deal with boundary value problems (prescribing Dirichlet or Neumann boundary conditions) for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation. First, we prove existence, uniqueness ...

We study the following nonlocal diffusion equation in the Heisenberg group Hn,ut(z,s,t)=J∗u(z,s,t)-u(z,s,t),where ∗ denote convolution product and J satisfies appropriated hypothesis. For the Cauchy problem we obtain that ...

In this paper we study a nonlocal diffusion problem on a manifold. These kinds of equations can model diffusions when there are long range effects and have been widely studied in Euclidean space. We first prove existence ...

We propose a numerical method to approximate the solution of a nonlocal diffusion problem on a general setting of metric measure spaces. These spaces include, but are not limited to, fractals, manifolds and Euclidean ...

In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction -up, p > 1 and set in ℝN. We consider a bounded, ...

This article in devoted to the study of the nonlocal dispersal equation

We study the large time behavior of solutions to a nonlocal diffusion equation, ut=J∗u−u with J smooth, radially symmetric and compactly supported, posed in R+ with zero Dirichlet boundary conditions. In the far-field ...