理论数学

Vol.2 No.2 (April 2012)

无界区域RN 上推广的B-BBM方程的长时间行为
Long Time Behavior of Solution for Generalized BBM Equation in RN

 

作者:

殷金翠 :太原理工大学数学学院

张建文

 

关键词:

无界区域kuratowskii http://chart.googleapis.com/chart?cht=tx&chl=%5Calpha%20" style="border:none" />- 非紧测度算子分解整体吸引子Unbounded Domain the kuratowskii http://chart.googleapis.com/chart?cht=tx&chl=%5Calpha%20" style="border:none" />- Non-Compact Measure Operator Decomposition Global Attractor

 

摘要:

本文研究了无界区域 上推广的B-BBM方程的长时间动力学行为。首先,利用Galerkin方法和对区域做极限的方法,验证了在无界区域 RN(n > 1)上解的存在唯一性;其次,通过算子分解技巧和加权范数的紧性以及kuratowskii -非紧测度,讨论了解的渐近光滑性;最后得到了该方程在无界区域H2 RN上整体吸引子的存在性。

The article presents the long time behavior of solution for the generalized BBM equation on unbounded domains. First, the existence and unique of the solutions on unbounded domains RN (n > 1) was proved by the Galerkin method and the method of the domain approximate. Secondly, operator decomposition method and the compactness of the weighted norm as well as kuratowskii - the non-compacted measure are applied to study the smooth property of the solution. Finally, the existence of the global attractor for the cor-responding semi-group on unbounded domains H2 RN was proved.

文章引用:

殷金翠 , 张建文 (2012) 无界区域RN 上推广的B-BBM方程的长时间行为。 理论数学, 2, 103-109. doi: 10.12677/pm.2012.22017

 

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