GUO Jiaxin,LI Chunhua.Time decay estimates of solutions to dissipative nonlinear Schr?dinger equations in two space dimensions[J].Journal of Yanbian University,2023,(04):283-287.
二维耗散非线性薛定谔方程解的时间衰减估计
- Title:
- Time decay estimates of solutions to dissipative nonlinear Schr?dinger equations in two space dimensions
- 文章编号:
- 1004-4353(2023)04-0283-05
- 关键词:
- 非线性薛定谔方程; 初值问题; 强耗散; Lq- 时间衰减估计
- Keywords:
- nonlinear Schr?dinger equations; initial value problem; strong dissipation; Lq- time decay estimates
- 分类号:
- O175.29
- 文献标志码:
- A
- 摘要:
- 研究了一类二维耗散非线性薛定谔方程初值问题解的时间衰减估计,其中非线性项为λ|v|p - 1v, λ为复常数,并且λ满足强耗散条件λ2<0, |λ2|≥(p-1)/(2p1/2)|λ1|.在初值大小不受限制的条件下,得到了上述二维耗散非线性薛定谔方程解的Lq- 时间衰减估计,其中q>2.
- Abstract:
- Time decay estimates of solutions to the initial value problem of nonlinear Schr?dinger equations in two space dimensions were studied, where the nonlinear term was λ|v|p - 1v, λ was a complex constant and λ satisfied the strong dissipative condition λ2<0, |λ2|≥(p-1)/(2p1/2)|λ1|.We obtained the Lq- time decay estimates of the solutions to the above nonlinear Schr?dinger equations without assuming the size restriction on the initial data, where q>2.
参考文献/References:
[1] KITA N, SHIMOMURA A.Asymptotic behavior of solutions to Schr?dinger equations with a subcritical dissipative nonlinearity [J].Journal of Differential Equations, 2007,242(1):192 - 210.
[2] OGAWA T, SATO T.L2 - decay rate for the critical nonlinear Schr?dinger equation with a small smooth data [J].Nonlinear Differential Equations and Applications, 2020,27:18.
[3] SATO T.L2 - decay estimate for the dissipative nonlinear Schr?dinger equation in the Gevrey class [J].Archiv der Mathematik, 2020,115(5):575 - 588.
[4] KITA N, SATO T.Optimal L2 - decay of solutions to a nonlinear Schr?dinger equation with sub - critical dissipative nonlinearity [J].Nonlinear Differential Equations and Applications, 2022,29:41.
[5] KITA N, SATO T.Optimal L2 - decay of solutions to the dissipative nonlinear Schr?dinger equation in higher space dimensions [J].Journal of Differential Equations, 2023,354:49 - 66.
[6] KATAYAMA S, LI C H, SUNAGAWA H.A remark on decay rates of solutions for a system of quadratic nonlinear Schr?dinger equations in 2D [J].Differential Integral Equations, 2014,27(3/4):301 - 312.
[7] KITA N, SHIMOMURA A.Large time behavior of solutions to Schr?dinger equations with a dissipative nonlinearity for arbitrarily large initial data [J].Journal of the Mathematical Society of Japan, 2009,61(1):39 - 64.
[8] JIN G Z, JIN Y F, LI C H.The initial value problem for nonlinear Schr?dinger equations with a dissipative nonlinearity in one space dimension [J].Journal of Evolution Equations, 2016,16(4):983 - 995.
[9] HAYASHI N, LI C H, NAUMKIN P I.Time decay for nonlinear dissipative Schr?dinger equations in optical fields [J].Advances in Mathematical Physics, 2016,2016:3702738.
[10] LIU X, ZHANG T.Modified scattering for the one - dimensional Schr?dinger equation with a subcritical dissipative nonlinearity [J].Journal of Dynamics and Differential Equations, 2023.https://doi.org/10.1007/s10884-023-10272- 4.
[11] HAYASHI N, NAUMKIN P I.Asymptotics for large time of solutions to the nonlinear Schr?dinger and Hartree equations [J].American Journal of Mathematics, 1998,120(2):369 - 389.
相似文献/References:
[1]韩琦悦,李春花*.一类非线性薛定谔方程解的衰减估计[J].延边大学学报(自然科学版),2020,46(01):24.
HAN Qiyue,LI Chunhua*.Decay estimates of solutions to a class of nonlinear Schr?dinger equations[J].Journal of Yanbian University,2020,46(04):24.
[2]马瑞,李春花.一类具有位势的二维非线性薛定谔系统解的渐近行为[J].延边大学学报(自然科学版),2021,47(04):283.
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备注/Memo
收稿日期: 2023-09-30
基金项目: 吉林省教育厅科学技术研究项目(JJKH20220527KJ)
第一作者: 郭佳鑫(1999—),女,硕士研究生,研究方向为微分方程及其应用.
通信作者: 李春花(1977—),女(朝鲜族),博士,副教授,研究方向为微分方程及其应用.