无界区域R^n上GBBM方程的指数吸引子

The Exponential Attractor for the GBBM Equations on Unbounded Domains R^n

研究了无界区域Rn(n 3)上GBBM方程的长时间动力学行为ut-aΔut-bΔu+F(u)+γu=h(x),x∈Rn,t∈R+,其中F(u)满足适当条件.应用算子分解技巧和构造加权空间上紧算子等方法,通过对方程的解作先验范数估计,证明了无界区域Rn(n 3)上GBBM方程指数吸引子的存在性.

This paper studied the long time behavior of solution for GBBM equations on the unbounded domains R^n（n〈3）ut-a△ut-b△u＋▽·F（u）＋ru=h（x）,x∈R^n,t∈R^＋,where ▽ F（u） satisfying given conditions. The existence of the exponential attractor for the corresponding semigroup was proved by the priori estimate. The method of the decomposition of operators and constructing compact operators with the compactness of the weighted spaces was used.