一类非线性Schrdinger方程的整体解和自相似解  

THE GLOBAL SOLUTIONS AND SELF-SIMILAR SOLUTIONS FOR A CLASS OF NONLINEAR SCHRDINGER EQUATIONS

作　　者：叶耀军[1] 王建平[2] 

机构地区：[1]浙江科技学院数学与信息科学系,杭州310023 [2]河南农业大学信息与计算科学系,郑州450002

出　　处：《系统科学与数学》2008年第6期751-757,共7页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10441002);河南省自然科学基金(0111051200);河南省青年骨干教师(2004-2006);河南省教育厅自然科学基金(2007110013)资助项目

摘　　要：对于α的某一取值范围,应用广义Strichartz不等式和压缩映射原理研究了初值在弱L^P空间中足够小的条件下,非线性Schrdinger方程Cauchy问题整体解和自相似解的存在性.The global Cauchy problem of nonlinear Schroedinger equations is considered by using generalized Strichartz inequalities and the contraction mapping principle. Under some restrictions on parameter α, if the initial value is sufficiently small in some weak L^p space, then there exists a global solution. Moreover, the global unique existence of self-similar solutions is obtained in weak L^p space for the small initial value with self-similar structure.

关 键 词：非线性SCHROEDINGER方程 广义Strichartz估计 自相似解 

分 类 号：O241.8[理学—计算数学]