2004-Fez conference on Differential Equations and Mechanics.
Electronic Journal of Differential Equations,
Conference 11, 2004, pp. 61-70.
Title: Doubly nonlinear parabolic equations related to the
p-Laplacian operator
Authors: Fatiha Benzekri (Faculte des sciences, Maroc)
Abderrahmane El Hachimi (Faculte des sciences, Maroc)
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.