EQUI-ATTRACTION AND BACKWARD COMPACTNESS OF PULLBACK ATTRACTORS FOR POINT-DISSIPATIVE GINZBURG-LANDAU EQUATIONS

作者：Li, Yangrong^*; She, Lianbing; Yin, Jinyan

来源：Acta Mathematica Scientia, 2018, 38(2): 591-609.

DOI：10.1016/S0252-9602(18)30768-9

• Non-autonomous systems
• point dissipative processes
• pullback attractors
• backward compact attractors
• equi-attractors
• Ginzburg-Landau equations

A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynamical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly hounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force.

• 出版日期2018-3
• 单位西华师范大学; 西南大学; 六盘水师范学院