top
Using the asymptotic a priori estimate method, we prove the existence of a pullback -attractor for a reaction-diffusion equation with an inverse-square potential in a bounded domain of (N ≥ 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 -attractor has a finite fractal dimension and is upper semicontinuous with respect to the parameter in the potential.
Cung The Anh, and Ta Thi Hong Yen. "Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials." Annales Polonici Mathematici 102.2 (2011): 161-186. <http://eudml.org/doc/280424>.
@article{CungTheAnh2011, abstract = {Using the asymptotic a priori estimate method, we prove the existence of a pullback -attractor for a reaction-diffusion equation with an inverse-square potential in a bounded domain of $ℝ^\{N\}$ (N ≥ 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 -attractor has a finite fractal dimension and is upper semicontinuous with respect to the parameter in the potential.}, author = {Cung The Anh, Ta Thi Hong Yen}, journal = {Annales Polonici Mathematici}, keywords = {fractal dimension; upper semicontinuity; compactness method; asymptotic a priori estimate; inverse-square potential}, language = {eng}, number = {2}, pages = {161-186}, title = {Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials}, url = {http://eudml.org/doc/280424}, volume = {102}, year = {2011}, }
TY - JOUR AU - Cung The Anh AU - Ta Thi Hong Yen TI - Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials JO - Annales Polonici Mathematici PY - 2011 VL - 102 IS - 2 SP - 161 EP - 186 AB - Using the asymptotic a priori estimate method, we prove the existence of a pullback -attractor for a reaction-diffusion equation with an inverse-square potential in a bounded domain of $ℝ^{N}$ (N ≥ 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 -attractor has a finite fractal dimension and is upper semicontinuous with respect to the parameter in the potential. LA - eng KW - fractal dimension; upper semicontinuity; compactness method; asymptotic a priori estimate; inverse-square potential UR - http://eudml.org/doc/280424 ER -