The Long Time Behavior Of Solution For The GBBM Equation On Unbounded Domains

This paper studied the GBBM equation with the damping term on unbounded domains Rn(n > 1)where a,b,r be positive constants, A be a Laplace operator, V be a ndimensionally gradient operator, F satisfy suitable conditions. Firstly, the existence and unique of the solutions H2 on unbounded domains R"(n > 1) was proved by the Galerkin method and the method of the domain approximate. Secondly, the long time behavior for the solution of the equation was considered. Using the operator decomposition method and the compactness of the weighted norm as well as Kuratowskii a -the non-compact measure, the existence of the global attractor for the corresponding semi-group on unbounded domains Rn(n>1) was obtained in charter 2. It was shown that there exists an exponential attractor on unbounded domains R"(n < 3) in charter 3.