Asymptotic behaviour for a diffusion equation governed by nonlocal interactions.

Armel Andami Ovono (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the parabolic problem $L^\infty $ estimates of solution based on using the Moser iterations and existence of global attractor. We finish our study by the issue of asymptotic behaviour in some cases when $t\rightarrow \infty$.

Mots clés: comparison principle; nonlocal problems; radial solutions; asymptotic behaviour

Domaines: Equations aux dérivées partielles [math.AP]

Armel Andami Ovono. Asymptotic behaviour for a diffusion equation governed by nonlocal interactions.. 2010. ⟨hal-00461572⟩