非经典扩散方程时间依赖吸引子的渐近结构

Asymptotic structure of time-dependent global attractors for the nonclassical diffusion equations

摘要:

非经典扩散方程主要源自非牛顿流体、固体力学以及热传导理论. 这类方程解的长时间行为及其渐近结构是一个重要的问题. 本文研究了非经典扩散方程时间依赖吸引子 $A_{t}$ 的渐近结构, 并获得了该吸引子的一个正则性结果, 推广和发展了2015年丁涛和刘永峰给出的一个结论.

Abstract:

Nonclassical reaction-diffusion equations mainly stem from non-Newtonian flows, solid mechanics, and heat conduction theories. The longtime behavior and asymptotic structure of solutions to these equations are important. We study the asymptotic structure of time-dependent global attractors $A_{t}$ associated with the nonclassical reaction-diffusion equations in this paper, and obtain the further regularity of attractors. All these extend and develop the result reported by T.Ding and Y.F.Liu in 2015.