非齐次非线性薛定谔方程新的爆破准则

李双双

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

doi: 10.3969/j.issn.1000-5641.201911029

李双双

西北师范大学数学与统计学院, 兰州　730070

基金项目: 国家自然科学基金(11601435)

详细信息

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

中图分类号: O175.29
计量
- 文章访问数: 112
- HTML全文浏览量: 50
- PDF下载量: 7
- 被引次数: 0
出版历程
- 收稿日期: 2019-06-26
- 网络出版日期: 2020-07-20
- 刊出日期: 2020-07-25

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

LI Shuangshuang

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

摘要

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.
- 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].
- nonhomogeneous nonlinear Schrödinger equation /
- invariant set /
- blow-up

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参考文献(15)

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