Geodesic
Existence and regularity of a global attractor for doubly nonlinear parabolic equations
Electronic journal of differential equations, Tome 2002 (2002)
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 
@article{EJDE_2002__2002__a143,
     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},
     year = {2002},
     volume = {2002},
     zbl = {0993.35021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a143/}
}
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%A El Ouardi,  Hamid
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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__a143/