耦合分数阶Klein-Gordon方程驻波的研究

IF 0.8 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal Pub Date : 2023-11-19 DOI:10.1515/gmj-2023-2089

Zhenyu Guo, Xin Zhang

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引用次数: 0

摘要

本文的目的是处理耦合非线性分数阶Klein-Gordon方程中的驻波问题。首先，我们建立了单个非线性分数阶拉普拉斯方程的约束极小化。然后用变分方法证明了具有基态的驻波的存在性。其次，应用势阱论证和凹度法，得到了爆破和全局存在的尖锐判据。最后，给出了驻波的不稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the standing wave in coupled fractional Klein–Gordon equation

Abstract The aim of this paper is to deal with the standing wave problems in coupled nonlinear fractional Klein–Gordon equations. First, we establish the constrained minimizations for a single nonlinear fractional Laplace equation. Then we prove the existence of a standing wave with a ground state using a variational argument. Next, applying the potential well argument and the concavity method, we obtain the sharp criterion for blowing up and global existence. Finally, we show the instability of the standing wave.

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来源期刊

Georgian Mathematical Journal 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.