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In this paper we study the asymptotic behaviour of a nonlocal nonlinearparabolic equation governed by a parameter. After giving the existence ofunique branch of solutions composed by stable solutions in stationary case, wegives for the parabolic problem $L^\infty $ estimates of solution based onusing the Moser iterations and existence of global attractor. We finish ourstudy by the issue of asymptotic behaviour in some cases when $t\to \infty$.

Asymptotic behaviour for a diffusion equation governed by nonlocal interactions.