无界区域R^1上Hirota型方程的全局吸引子

Global Attractor for Hirota Equation in Unbounded Domain R^1

研究了无界区域R1上Hirota型方程解的长时间行为,首先采用能量方法证明了H1(R1)中有界吸收集的存在性,然后利用算子分解方法克服了无界区域嵌入不紧性的困难,从而证明H1(R1)强拓扑下的全局吸引子的存在性,即将Hirota型方程解的全局吸引子从有界区域推广到无界区域.

We study the long-time behaviour of solution to Hirota equation in unboumded domain R1.Firstly,we use energy methods to prove the existence of the absorbing set in H1 （R1）,then use the decomposition of operators to overcome the difficulties of the embeddings＇ uncompactness in unbounded domains.Thus we obtain the existence of global attractor for the strong topology of H1 （R1）.That is,we extend the existence of global attractor from bounded domains to unbounded domains.