Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 45, pp. 1-15.
Title: Existence and regularity of a global attractor for
doubly nonlinear parabolic equations
Authors: Abderrahmane El Hachimi (Faculte des Sciences, El Jadida - Maroc)
Hamid El Ouardi (Faculte des Sciences, El Jadida - Maroc)
Abstract:
In this paper we consider a doubly nonlinear parabolic partial
differential equation
$$
\frac{\partial \beta (u)}{\partial t}-\Delta _{p}u+f(x,t,u)=0
\quad \hbox{in }\Omega \times\mathbb{R}^{+},
$$
with Dirichlet boundary condition and initial data given.
We prove the existence of a global compact attractor
by using a dynamical system approach. Under additional
conditions on the nonlinearities $\beta$, $f$, and on $p$,
we prove more regularity for the global attractor
and obtain stabilization results for the solutions.
Submitted January 15, 2001. Published May 24, 2002.
Math Subject Classifications: 35K15, 35K60, 35K65.
Key Words: p-Laplacian; a-priori estimate; long time behaviour;
dynamical system; absorbing set; global attractor.