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.

Show me the PDF file (241K), TEX file, and other files for this article.

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

Return to the EJDE web page