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。

Abstract: 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

参考文献

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