2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco.
Electron. J. Diff. Eqns., Conference 14 (2006), pp. 9-20.

Existence result for variational degenerated parabolic problems via pseudo-monotonicity

Lahsen Aharouch, Elhoussine Azroul, Mohamed Rhoudaf

Abstract:
In this paper, we study the existence of weak solutions for the initial-boundary value problems of the nonlinear degenerated parabolic equation
$$ \frac{\partial u}{\partial t}-\hbox{\rm div}a(x,t,u,\nabla u) +a_0(x,t,u,\nabla u) = f , $$
where $Au = -\hbox{\rm div}a(x,t,u,\nabla u)$ 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.

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Lahsen Aharouch
Département de Mathématiques et Informatique
Faculté des Sciences Dhar-Mahraz
B.P 1796 Atlas Fès, Maroc
email: l_aharouch@yahoo.fr
Elhoussine Azroul
Département de Mathématiques et Informatique
Faculté des Sciences Dhar-Mahraz
B.P 1796 Atlas Fès, Maroc
email: azroul_elhoussine@yahoo.fr
Mohamed Rhoudaf
Département de Mathématiques et Informatique
Faculté des Sciences Dhar-Mahraz
B.P 1796 Atlas Fès, Maroc
email: rhoudaf_mohamed@yahoo.fr

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