Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials

Cung The Anh¹ ; Ta Thi Hong Yen²

¹ Department of Mathematics Hanoi National University of Education 136 Xuan Thuy, Cau Giay Hanoi, Vietnam
² Department of Mathematics Hanoi Pedagogical University No. 2 Xuan Hoa, Phuc Yen Vinhphuc province, Vietnam

Annales Polonici Mathematici, Tome 102 (2011) no. 2, pp. 161-186.

Résumé

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.

Détail

DOI : 10.4064/ap102-2-5

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