Electron. J. Diff. Eqns., Vol. 2002(2002), No. 45, pp. 1-15.

Existence and regularity of a global attractor for doubly nonlinear parabolic equations

Abderrahmane El Hachimi & Hamid El Ouardi

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.

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Abderrahmane El Hachimi
UFR Mathematiques Appliquees et Industrielles
Faculte des Sciences
B.P. 20, El Jadida - Maroc
e-mail: elhachimi@ucd.ac.ma
Hamid El Ouardi
Ecole Nationale Superieure d'Electricite et de Mecanique
B.P. 8118 -Casablanca-Oasis, Maroc
and
UFR Mathematiques Appliquees et Industrielles
Faculte des Sciences
B.P. 20, El Jadida - Maroc
e-mail: elouardi@ensem-uh2c.ac.ma

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