Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials
Annales Polonici Mathematici, Tome 102 (2011) no. 2, pp. 161-186
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Using the asymptotic a priori estimate method, we prove the existence of a pullback $\mathcal{D}$-attractor for a reaction-diffusion equation with an inverse-square potential in a bounded domain of $\mathbb{R}^{N}$ $(N\geq 3)$, with the nonlinearity of polynomial type and a suitable exponential growth of the external force. Then under some additional conditions, we show that the pullback $\mathcal{D}$-attractor has a finite fractal dimension and is upper semicontinuous with respect to the parameter in the potential.
Keywords:
using asymptotic priori estimate method prove existence pullback mathcal attractor reaction diffusion equation inverse square potential bounded domain mathbb geq nonlinearity polynomial type suitable exponential growth external force under additional conditions pullback mathcal attractor has finite fractal dimension upper semicontinuous respect parameter potential
Affiliations des auteurs :
Cung The Anh 1 ; Ta Thi Hong Yen 2
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author = {Cung The Anh and Ta Thi Hong Yen},
title = {Finite-dimensional pullback attractors for parabolic equations with {Hardy} type potentials},
journal = {Annales Polonici Mathematici},
pages = {161--186},
publisher = {mathdoc},
volume = {102},
number = {2},
year = {2011},
doi = {10.4064/ap102-2-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap102-2-5/}
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Cung The Anh; Ta Thi Hong Yen. Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials. Annales Polonici Mathematici, Tome 102 (2011) no. 2, pp. 161-186. doi: 10.4064/ap102-2-5
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