2004-Fez conference on Differential Equations and Mechanics. Electron. J. Diff. Eqns., Conference 11, 2004, pp. 61-70.

Doubly nonlinear parabolic equations related to the p-Laplacian operator

Fatiha Benzekri, Abderrahmane El Hachimi

Abstract:
This paper concerns the doubly nonlinear parabolic P.D.E.
$$ \frac{\partial\beta(u)} {\partial t}-\Delta_p u + f(x,t,u )= 0 \quad \hbox{ in } \Omega\times\mathbb{R}^+, $$
with Dirichlet boundary conditions and initial data. We investigate here a time-discretization of the continuous problem by the Euler forward scheme. In addition to existence, uniqueness and stability questions, we study the long-time behavior of the solution to the discrete problem. We prove the existence of a global attractor, and obtain regularity results under certain restrictions.

Published October 15, 2004.
Math Subject Classifications: 35K15, 35K60, 35J60.
Key Words: p-Laplacian; nonlinear parabolic equations; semi-discretization; discrete dynamical system; attractor.

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Fatiha Benzekri
UFR Mathématiques Appliquées et Industrielles
Faculté des sciences
B. P. 20, El Jadida, Maroc
email: benzekri@ucd.ac.ma
Abderrahmane El Hachimi
UFR Mathématiques Appliquées et Industrielles
Faculté des Sciences
B.P. 20, El Jadida, Maroc
e-mail: elhachimi@ucd.ac.ma

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