Large time behavior of solutions to Schrödinger equations with a dissipative nonlinearity for arbitrarily large initial data
Large time behavior of solutions to Schrödinger equations with a dissipative nonlinearity for arbitrarily large initial data
复制标题
DOI：
10.2969/jmsj/06110039
复制
发表时间：
2009
影响因子：
0.7
通讯作者：
Naoyasu Kita;A. Shimomura
中科院分区：
文献类型：
--
作者：
Naoyasu Kita;A. Shimomura
研究了具有长程耗散非线性项λ的非线性Schrodinger方程Cauchy问题解的时间渐近性态|u| p − 1 u在一维空间中，其中1 < p ≤ 3（即p是临界或次临界指数），λ是复常数，满足Im λ < 0和（（p − 1）/ 2 p）|R e λ| ≤ |I m λ| .当“p = 3“或“p < 3且p适当地接近3“时，我们给出了任意大初始数据下解的时间衰减估计和大时间渐近性。
We study the asymptotic behavior in time of solutions to the Cauchy problem of nonlinear Schrodinger equations with a long-range dissipative nonlinearity given by λ | u | p − 1 u in one space dimension, where 1 < p ≤ 3 (namely, p is a critical or subcritical exponent) and λ is a complex constant satisfying Im λ < 0 and ( ( p − 1 ) / 2 p ) | R e λ | ≤ | I m λ | . We present the time decay estimates and the large-time asymptotics of the solution for arbitrarily large initial data, when “ p = 3 ” or “ p < 3 and p is suitably close to 3 ”.