带耗散的广义Camassa-Holm方程的吸引子  

The Attractor of A General Camassa-Holm Equation with Dissipative

作　　者：谌德[1] 向新民[1] 

机构地区：[1]上海师范大学数理信息学院,上海200234

出　　处：《应用数学与计算数学学报》2008年第2期19-27,共9页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(10371077;10771142)

摘　　要：讨论了一类带耗散的广义Camassa-Holm方程．先将方程的解以及初始条件化为积分平均为零，然后建立与原问题相应的周期初值问题近似解的先验估计，由此得到原问题解的存在唯一性，并证明了在H^2per（Ω）中吸引子的存在性．A general Camassa-Holm equation with dissipative is disscussed. At first , the integral average of the solution and the initial function is transformed into 0, then the prior estimation of the solution of the periodic initial problem derived from the original problem is constructeded , thus the existence and uniqueness of the solution of the original problem is obtained. At last the existence of the global attractor in H^2per （Ω） is proved.

关 键 词：广义CAMASSA-HOLM方程 周期初值问题 先验估计 整体吸引子 

分 类 号：O175.29[理学—数学]