2021年5月
Strong blow-up instability for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations
Discrete & Continuous Dynamical Systems
- 巻
- 41
- 号
- 5
- 開始ページ
- 2411
- 終了ページ
- 2445
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.3934/dcds.2020370
This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power type nonlinearity, stability and instability for standing wave solutions have been extensively studied. On the other hand, in the case of our system, there are no results concerning the stability and instability as far as we know. In this paper, we prove strong blow-up instability for the standing wave to our system. The proof is based on the techniques in Ohta and Todorova [25]. It turns out that we need the mass resonance condition in two or three space dimensions whose cases are the mass-subcritical case.
- リンク情報
-
- DOI
- https://doi.org/10.3934/dcds.2020370
- 共同研究・競争的資金等の研究課題
- 非線型分散型方程式における散乱理論の新展開
- 共同研究・競争的資金等の研究課題
- 非線形Klein-Gordon方程式の連立系における解の大域挙動の解明
- 共同研究・競争的資金等の研究課題
- 非線型分散型偏微分方程式における解の性質や長時間挙動の解明
- URL
- https://arxiv.org/abs/1911.08157
- ID情報
-
- DOI : 10.3934/dcds.2020370