Global Attractors for a Class of Semilinear Degenerate Parabolic Equations on $\mathbb R^N$
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 1, pp. 47-65
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove the existence of global attractors for the following semilinear degenerate parabolic equation on $\mathbb R^N$:
$$ \frac{\partial u}{\partial t} - \text{div}(\sigma (x)\nabla u) + \lambda u+ f(x,u) = g(x),$$
under a new condition concerning the variable nonnegative diffusivity $\sigma(\cdot)$ and for an arbitrary polynomial growth order of the nonlinearity $f$. To overcome some difficulties caused by the lack of compactness of the embeddings, these results are proved by combining the tail estimates method and the asymptotic a priori estimate method.
Keywords:
prove existence global attractors following semilinear degenerate parabolic equation mathbb frac partial partial text div sigma nabla lambda under condition concerning variable nonnegative diffusivity sigma cdot arbitrary polynomial growth order nonlinearity overcome difficulties caused lack compactness embeddings these results proved combining tail estimates method asymptotic priori estimate method
Affiliations des auteurs :
Cung The Anh 1 ; Le Thi Thuy 2
@article{10_4064_ba61_1_6,
author = {Cung The Anh and Le Thi Thuy},
title = {Global {Attractors} for a {Class} of {Semilinear} {Degenerate} {Parabolic} {Equations} on $\mathbb R^N$},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {47--65},
publisher = {mathdoc},
volume = {61},
number = {1},
year = {2013},
doi = {10.4064/ba61-1-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba61-1-6/}
}
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Cung The Anh; Le Thi Thuy. Global Attractors for a Class of Semilinear Degenerate Parabolic Equations on $\mathbb R^N$. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 1, pp. 47-65. doi: 10.4064/ba61-1-6
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