Electron. J. Diff. Equ., Vol. 2010(2010), No. 134, pp. 1-16.

Asymptotic behaviour for a diffusion equation governed by nonlocal interactions

Armel Andami Ovono

In this article, 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 $t\to \infty$.

Submitted March 9, 2010. Published September 20, 2010.
Math Subject Classifications: 35B35, 35B40, 35B51.
Key Words: Comparison principle; nonlocal diffusion; branch of solutions; asymptotic behaviour.

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Armel Andami Ovono
L.A.M.F.A CNRS UMR 6140, 33 rue Saint Leu
80039 Amiens cedex 1, France
email: andami@u-picardie.fr

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