非齐次非线性薛定谔方程新的爆破准则

doi:10.3969/j.issn.1000-5641.201911029

华东师范大学学报（自然科学版） ›› 2020, Vol. 2020 ›› Issue (4): 64-71.doi: 10.3969/j.issn.1000-5641.201911029

非齐次非线性薛定谔方程新的爆破准则

李双双

西北师范大学数学与统计学院, 兰州 730070

收稿日期:2019-06-26 发布日期:2020-07-20
作者简介:李双双, 女, 硕士研究生, 研究方向为偏微分方程. E-mail: 18793114195@163.com
基金资助:
国家自然科学基金(11601435)

A new blow-up criterion for the nonhomogeneous nonlinear Schrödinger equation

LI Shuangshuang

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2019-06-26 Published:2020-07-20

摘要/Abstract

摘要： 本文研究了非齐次非线性薛定谔方程爆破解的存在性. 首先构造了一类不变集, 然后应用最佳Gagliardo-Nirenberg型不等式以及仔细的分析证明了对任意大的$\mu$, 存在$u_{0}\in H^{1}$, 使得$E(u_{0})=\mu$, 并且以$u_{0}$为初值的解$u(t,x)$在有限时间内爆破, 该结果改进了文献[1]中的结果.

关键词: 非齐次非线性薛定谔方程, 不变集合, 爆破

Abstract: In this paper, the existence of blow-up solutions for the nonhomogeneous nonlinear Schrödinger equation is studied. First, a class of invariant sets is constructed and then the optimal Gagliardo-Nirenberg type inequality is applied; careful analysis is used to prove that for any large $\mu$, there exists $u_{0}\in H^{1}$ so that $E(u_{0})=\mu$ and the solution $u(t,x)$ with $u_{0}$ as an initial value blows up in finite time. This result supplements the existing content in the literature [1].

Key words: nonhomogeneous nonlinear Schrödinger equation, invariant set, blow-up

中图分类号:

O175.29

李双双. 非齐次非线性薛定谔方程新的爆破准则[J]. 华东师范大学学报（自然科学版）, 2020, 2020(4): 64-71.

LI Shuangshuang. A new blow-up criterion for the nonhomogeneous nonlinear Schrödinger equation[J]. Journal of East China Normal University(Natural Science), 2020, 2020(4): 64-71.

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非齐次非线性薛定谔方程新的爆破准则

A new blow-up criterion for the nonhomogeneous nonlinear Schrödinger equation

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