Geodesic
Pullback attractor for non-autonomous $p$-Laplacian equations with dynamic flux boundary conditions
Electronic Journal of Differential Equations, Tome 2014 (2014).

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

Summary: This article studies the long-time asymptotic behavior of solutions for the non-autonomous $$ u_t-\Delta_pu+ |u|^{p-2}u+f(u)=g(x,t) $$ with dynamic flux boundary conditions $$ u_t+|\nabla u|^{p-2}\frac{\partial u}{\partial\nu}+f(u)=0 $$ in a n-dimensional bounded smooth domain $\Omega$ under some suitable assumptions. We prove the existence of a pullback attractor in $\big(W^{1,p}(\Omega)\cap L^q(\Omega)\big)\times L^q(\Gamma)$ by asymptotic a priori estimate.
Classification : 35B40, 37B55
Keywords: pullback attractor, Sobolev compactness embedding, p-Laplacian, norm-to-weak continuous process, asymptotic a priori estimate, non-autonomous, nonlinear flux boundary conditions 
@article{EJDE_2014__2014__a66,
     author = {You, Bo and Li, Fang},
     title = {Pullback attractor for non-autonomous $p${-Laplacian} equations with dynamic flux boundary conditions},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a66/}
}
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You, Bo; Li, Fang. Pullback attractor for non-autonomous $p$-Laplacian equations with dynamic flux boundary conditions. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a66/