全直线上非线性BBM方程Cauchy问题解的存在唯一性  

The existence and uniqueness of the global solution for the cauchy problem for the nonlinear BBM equation on the whole line

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：《上海师范大学学报（自然科学版）》2005年第3期7-10,共4页Journal of Shanghai Normal University(Natural Sciences)

基　　金：国家自然科学基金(10371077)上海市教委科学技术发展基金(03DZ21)资助项目.

摘　　要：讨论了全直线上非线性BBM方程Cauchy问题解的存在唯一性.先用CaJerkin方法建立与原问题相应的周期初值问题近似解的先验估计,由紧性方法得到周期初值问题的解,然后利用该近似解的先验估计与周期D无关的性质,由对角线选取方法及令D→∞得到原问题广义解的存在性.Studies the existence and uniqueness of the global solution to the Cauchy problem for the nonlinear BBM equation on the whole line. First we construct a periodic initial - value problem corresponding to the primitive problem by virtue of the Galerkin method, and obtain the prior estimation of the approximate solution. Using the method of compactness we get the solution of the periodic initial - value problem. Then we use the property that the prior estimation of the approximate solution is independent of the period D. By the diagonal method and letting D→∞ , we get the existence to the general solution to the primitive problem.

关 键 词：非线性BBM方程 周期初值问题 紧致性原理 

分 类 号：O175.1[理学—数学]