Geodesic
Existence and regularity of a global attractor for doubly nonlinear parabolic equations
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we consider a doubly nonlinear parabolic partial differential equation $$ \frac{\partial \beta (u)}{\partial t}-\Delta _{p}u+f(x,t,u)=0 \quad \hbox{in }\Omega \times\mathbb{R}^{+}, $$ with Dirichlet boundary condition and initial data given. We prove the existence of a global compact attractor by using a dynamical system approach. Under additional conditions on the nonlinearities $\beta, f$, and on $p$, we prove more regularity for the global attractor and obtain stabilization results for the solutions.
Classification : 35K15, 35K60, 35K65
Keywords: p-Laplacian, a-priori estimate, long time behaviour, dynamical system, absorbing set, global attractor 
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     author = {El Hachimi, Abderrahmane and El Ouardi, Hamid},
     title = {Existence and regularity of a global attractor for doubly nonlinear parabolic equations},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a43/}
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El Hachimi, Abderrahmane; El Ouardi, Hamid. Existence and regularity of a global attractor for doubly nonlinear parabolic equations. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a43/