Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 113, pp. 1-14.
Title: Doubly nonlinear parabolic equations related to the
p-Laplacian operator: Semi-discretization
Authors: Fatiha Benzekri (Faculte des sciences, El Jadida, Maroc)
Abderrahmane El Hachimi (Faculte des sciences, El Jadida, Maroc)
Abstract:
We study the doubly nonlinear parabolic equation
$$
\frac{\partial\beta(u)} {\partial t}-\triangle_p u + f(x,t,u )= 0
\quad\hbox{in } \Omega\times\mathbb{R}^+,
$$
with Dirichlet boundary conditions and initial data.
We investigate a time-discretization of the continuous
problem by the Euler forward scheme. In addition to proving
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 its
regularity under additional conditions.
Submitted April 16, 2003. Published November 11, 2003.
Math Subject Classifications: 35K15, 35K60, 35J60.
Key Words: P-Laplacian; nonlinear parabolic equations;
semi-discretization; discrete dynamical system; attractor.