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 ...

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 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 ...

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 ...

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, ...

We introduce and analyze a nonlocal free boundary problem which may be of interest to describe the spreading of populations in hostile environments. The rate of growth of the volume of the region occupied by the population ...

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 ...

In this paper we consider a fixed initial condition u(0) and we study the limit as epsilon -> 0 of u(epsilon), the solution to the re-scaled problem

We consider the nonlocal evolution Dirichlet problem u(t)(x, t) = f(Omega) J(x-y/g(y)) u(y, t)/g(y)(N) dy- u(x, t), x is an element of Omega, t > 0; u = 0, x is an element of R-N\Omega, t >= 0; u(x, 0) = u(0)(x), x is an ...