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Asymptotic behaviour for a diffusion equation governed by nonlocal interactions. (English) Zbl 1203.35042

Summary: 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 \(t\to \infty\).

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35B35 Stability in context of PDEs
35B51 Comparison principles in context of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35K59 Quasilinear parabolic equations
35B41 Attractors
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