Asymptotic behaviour for a diffusion equation governed by nonlocal interactions

Details Asymptotic behaviour for a diffusion equation governed by nonlocal interactions Asymptotic behaviour for a diffusion equation governed by nonlocal interactions

2010-04-29

arxiv.org/abs/1004.5297v1

Mathematics

Analysis of PDEs

19pp

Scientific paper

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 $t\to \infty$.

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