Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials
Tom 102 / 2011
Annales Polonici Mathematici 102 (2011), 161-186
MSC: Primary 35B41; Secondary 35K65, 35D05.
DOI: 10.4064/ap102-2-5
Streszczenie
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.
