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

Volume 102 / 2011

Cung The Anh, Ta Thi Hong Yen Annales Polonici Mathematici 102 (2011), 161-186 MSC: Primary 35B41; Secondary 35K65, 35D05. DOI: 10.4064/ap102-2-5

Abstract

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.

Authors

  • Cung The AnhDepartment of Mathematics
    Hanoi National University of Education
    136 Xuan Thuy, Cau Giay
    Hanoi, Vietnam
    e-mail
  • Ta Thi Hong YenDepartment of Mathematics
    Hanoi Pedagogical University No. 2
    Xuan Hoa, Phuc Yen
    Vinhphuc province, Vietnam
    e-mail

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