Asymptotic behavior of solutions to Schrödinger equations with a subcritical dissipative nonlinearity
Asymptotic behavior of solutions to Schrödinger equations with a subcritical dissipative nonlinearity
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DOI：
10.1016/j.jde.2007.07.003
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发表时间：
2007-11
影响因子：
2.4
通讯作者：
Naoyasu Kita;A. Shimomura
中科院分区：
文献类型：
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作者：
Naoyasu Kita;A. Shimomura
研究了具有亚临界耗散非线性项λ的非线性薛定谔方程初值问题解的时间渐近性态|u| p−1u，其中1<p<1+2/n，n是空间维数，λ是满足Imλ<0的复常数。当空间维数n ≠ 3，p充分接近1+2/n，初始数据充分小时，我们给出了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 initial value problem of the nonlinear Schrödinger equation with a subcritical dissipative nonlinearity λ|u|p−1u, where 1<p<1+2/n, n is the space dimension and λ is a complex constant satisfying Imλ<0. We show the time decay estimates and the large-time asymptotics of the solution, when the space dimension n⩽3, p is sufficiently close to 1+2/n and the initial data is sufficiently small.