非自治Reaction-Diffusion方程的后向紧吸引子的正则性

Regularity of Backward Compact Pullback Attractorsfor Non-autonomous Reaction-Diffusion Equations

运用后向Gronwall型不等式及一个后向截断的方法,在g是后向绝对连续的假设条件下,证明非自治Reaction-Diffusion方程在正则p(p≥2)次可积空间上存在唯一的后向紧拉回吸引子,这种紧性体现了非自治系统关于时间依赖的独特性,展示了非自治系统和自治系统的本质区别.

Combing a backward Gronwall-type inequality and a truncation technique,we show that the non-autonomous Reaction-Diffusion equation has a unique backward compact pullback attractor in p(p≥2)-time integrable spaces when the time-dependent force is backward absolutely continuous.This backward compactness of the attractor reflects the time-dependent feature of the non-autonomous dynamical system,and reveals the essential distinction between non-autonomous systems and autonomous systems.