无界区域R^N 上推广的B-BBM方程的长时间行为

Long Time Behavior of Solution for Generalized BBM Equation in R^N

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 R^N(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 R^N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 R^N (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 R^N was proved.