Title: Global attractor for a quasilinear parabolic equation of mean curvature type

Authors: Mitsuhiro Nakao, Naimah Aris

Addresses: Graduate School of Mathematics, Kyushu University, Fukuoka 810-8560, Japan. ' Graduate School of Mathematics, Kyushu University, Fukuoka 810-8560, Japan

Abstract: We prove the existence and some properties of global attractor in L^q with q > N and q ≥ 2 for the quasilinear parabolic equation u_t – div(σ(|∇u|²)∇u) + λu + g(x, u) = f(x) in a bounded domain in R^N where λ > 0 and σ (ν²) is a function like σ (ν²) = 1/√1 + ν². The problem in R^N is also considered.

Keywords: global attractors; nonlinear parabolic equations; mean curvature.

DOI: 10.1504/IJDSDE.2007.013747

International Journal of Dynamical Systems and Differential Equations, 2007 Vol.1 No.1, pp.75 - 84

Published online: 23 May 2007 *

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