Ovono, Armel Andami Asymptotic behaviour for a diffusion equation governed by nonlocal interactions. (English) Zbl 1203.35042 Electron. J. Differ. Equ. 2010, Paper No. 134, 16 p. (2010). 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 \(t\to \infty\). Cited in 7 Documents 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 Keywords:nonlocal diffusion; \(L^\infty\) estimates; Moser iterations PDFBibTeX XMLCite \textit{A. A. Ovono}, Electron. J. Differ. Equ. 2010, Paper No. 134, 16 p. (2010; Zbl 1203.35042) Full Text: arXiv EuDML EMIS