Non-local diffusion

Non-local Diffusion

Boundary Fluxes for Non-local Diffusion

Abstract. 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 existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we l...

Some non-local problems with nonlinear diffusion

In this paper we study different problems with nonlinear diffusion and non-local terms, some of them arising in population dynamics. We are able to give a complete description of the set of positive solutions and their stability. For that we employ a fixed point argument for the existence and uniqueness or multiplicity results and the study of singular eigenvalue problems for stability.

Some Non-Local Population Models with Non-Linear Diffusion

In this paper we present some theoretical results concerning to a non-local elliptic equation with non-linear diffusion arising from population dynamics.

Stability of Localized Structures in Non-local Reaction-diffusion Equations

The stability of non-homogeneous, steady state solutions of a scalar, non-local reaction-diffusion equation is considered. Sufficient conditions are provided that guarantee that the relevant linear operator possesses a countable infinity of discrete eigenvalues. These eigenvalues are shown to interlace the eigenvalues of a related local Sturm-Liouville operator. An oscillation theorem for the c...