2005-Oujda International Conference on Nonlinear Analysis,
Oujda, Morocco.
Electronic Journal of Differential Equations,
Conference 14 (2006), pp. 9-20.
Title: Existence result for variational degenerated parabolic
problems via pseudo-monotonicity
Authors: Lahsen Aharouch (Faculte des Sciences, Fez, Maroc)
Elhoussine Azroul (Faculte des Sciences, Fez, Maroc)
Mohamed Rhoudaf (Faculte des Sciences, Fez, Maroc)
Abstract:
In this paper, we study the existence of weak solutions for the
initial-boundary value problems of the nonlinear degenerated
parabolic equation
$$
\frac{\partial u}{\partial t}-\mathop{\rm div}a(x,t,u,\nabla u)
+a_0(x,t,u,\nabla u) = f ,
$$
where $Au = -\mathop{\rm div}a(x,t,u,\nabla u)$ is a classical
divergence operator of Leray-lions acting from
$L^p(0,T,W_0^{1,p}(\Omega,w))$ to its dual.
The source term $f$ is assumed to belong to
$L^{p'}(0,T,W^{-1,p'}(\Omega,w^*))$.
Published September 20, 2006.
Math Subject Classifications: 35J60.
Key Words: Weighted Sobolev spaces; boundary value problems;
truncations; parabolic problems.