Séminaire d'AnalyseNonlocal problem in metric measure spaces
Silvia Sastre-Gomez (UCM)
jeudi 02 octobre 2014 11:00 - Tours - Salle 1180 (Bât E2)
In this talk we study the existence, uniqueness, comparison properties and asymptotic behaviour of the solutions of some nonlocal diffusion problems. All the problems in this work are set in metric measure spaces. These spaces include very different type of spaces, for example, open subsets in R^N, graphs, manifolds, multistructures or some fractal sets. First of all we study the solutions of the linear nonlocal diffusion problem. In particular we describe the asymptotic behaviour using spectral methods. After that we will study the nonlinear nonlocal diffusion problem with a local reaction. In particular, we prove weak and strong maximum principles and the existence of two extremal equilibria, which attract the asymptotic dynamics of the solutions.