半无界区域上半线性薛定谔方程初边值问题解的破裂及其生命跨度的估计

数学物理学报 ›› 2016, Vol. 36 ›› Issue (6): 1186-1195.

半无界区域上半线性薛定谔方程初边值问题解的破裂及其生命跨度的估计

耿金波¹, 杨珍珍¹, 赖宁安²

1. 浙江师范大学数学系浙江金华 321004;
2. 丽水学院数学系浙江丽水 323000

收稿日期:2016-05-07 修回日期:2016-09-28 出版日期:2016-12-26 发布日期:2016-12-26
通讯作者: 赖宁安 E-mail:hyayue@gmail.com
基金资助:
国家自然科学基金（11501273）和浙江省自然科学基金（LQ13A010013，LY14A010010，LY14A010005）资助

Blow up and Lifespan Estimates for Initial Boundary Value Problem of Semilinear Schrödinger Equations on Half-Life

Geng Jinbo¹, Yang Zhenzhen¹, Lai Ning-An²

1. Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 321004;
2. Department of Mathematics, Lishui University, Zhejiang Lishui 323000

Received:2016-05-07 Revised:2016-09-28 Online:2016-12-26 Published:2016-12-26
Supported by:
Supported by the NSFC (11501273) and the Natural Science Foundation of Zhejiang Province (LQ13A010013,LY14A010010,LY14A010005)

摘要/Abstract

摘要：

该文主要研究了半无界区域上一维半线性薛定谔方程初边值问题解的破裂及其生命跨度估计.当非线性项指数p满足1 < p≤2时，证明了解在有限时间内破裂；当1 < p < 2时，进一步得到了解的生命跨度上界估计.证明的过程主要运用了试探函数方法.

关键词: 半线性薛定谔方程, 破裂, 生命跨度

Abstract:

In this paper, we consider the initial boundary value problem of semilinear Schrödinger equation on half-line. Blow up result will be established, assuming the power of the nonlinear term satisfying 1 < p≤2. Furthermore, we obtain the upper bound of the lifespan in the case 1 < p < 2. The proof is based on a contradiction argument, by constructing a special test function.

Key words: Semilinear Schrödinger equation, Blow up, Lifespan

中图分类号:

O212.62

耿金波, 杨珍珍, 赖宁安. 半无界区域上半线性薛定谔方程初边值问题解的破裂及其生命跨度的估计[J]. 数学物理学报, 2016, 36(6): 1186-1195.

Geng Jinbo, Yang Zhenzhen, Lai Ning-An. Blow up and Lifespan Estimates for Initial Boundary Value Problem of Semilinear Schrödinger Equations on Half-Life[J]. Acta mathematica scientia,Series A, 2016, 36(6): 1186-1195.

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