摘要
研究无界域上非自治p-Laplacian系统u_t-div(ε(t)|▽u|^(p-2)▽u)+f(x,u)=g(x)的长时间动力学行为。在带参变量t的赋范空间中,建立方程所对应过程在拉回意义下吸收集的存在性。在无界区域上研究方程所对应的无穷维动力系统,最大的困难在于Sobolev嵌入缺乏紧性。为克服Sobolev嵌入缺乏紧性,利用一致"tail"估计,证明系统所对应的过程是渐近紧的,从而得到依赖于时间t的全局吸引子的存在性。
The long time dynamical behavior of the non-autonomous p-Laplacian systems ut-div（ε（t） ｜Vu｜p-2 vu） ＋f（x, u） = g（x） is studied. In normed space with parameter t, it establishes the existence of absorbing sets. Studying infinite dimensional dynamical systems corresponding equation on unbounded domains, the biggest difficulty is the lacking compact of Sobolev embedding. In order to overcome the lacking compact of Sobolev imbedding, it is proved that the process associated with the system is asymp- totic compactness by using uniform estimates on the tails of solutions, then get the existence of time-de- pendent global attractor.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2016年第2期181-186,共6页
Journal of Natural Science of Heilongjiang University
基金
国家自然科学基金资助项目(11571092)
