Global attractor for a quasilinear parabolic equation of mean curvature type

Abstract

We prove the existence and some properties of global attractor in Lq with q > N and q ≥ 2 for the quasilinear parabolic equation ut div(σ('∇u')∇u) + λu + g(x, u) = f(x) in a bounded domain in RN where λ > 0 and σ (ν) is a function like σ (ν) = 1/√1 + ν. The problem in RN is also considered.

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