scholarly journals Strong instability of standing waves for nonlinear Klein-Gordon equations

2005 ◽  
Vol 12 (2) ◽  
pp. 315-322 ◽  
Author(s):  
Masahito Ohta ◽  
◽  
Grozdena Todorova ◽  
Keyword(s):  
Standing Waves ◽  
Strong Instability ◽  
Klein Gordon

A note on strong instability of standing waves for some semilinear wave and heat equations

2017 ◽  
Vol 165 (1) ◽  
pp. 53-68
Author(s):  
T. SAANOUNI
Keyword(s):  
Ground State ◽  
Initial Value Problems ◽  
Standing Waves ◽  
Heat Equations ◽  
Initial Value ◽  
Strong Instability ◽  
Two Space Dimensions

AbstractThe initial value problems for some semilinear wave and heat equations are investigated in two space dimensions. By proving the existence of ground state, strong instability of standing waves for the associated wave and heat equations are obtained.

scholarly journals Blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation

2020 ◽  
Vol 10 (1) ◽  
pp. 311-330 ◽  
Author(s):  
Feng Binhua ◽  
Ruipeng Chen ◽  
Jiayin Liu
Keyword(s):  
Blow Up ◽  
Standing Waves ◽  
Radial Solutions ◽  
Choquard Equation ◽  
Decomposition Theory ◽  
Profile Decomposition ◽  
Strong Instability

Abstract In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation $$\begin{array}{} \displaystyle i\partial_t\psi- (-{\it\Delta})^s \psi+(I_\alpha \ast |\psi|^{p})|\psi|^{p-2}\psi=0. \end{array}$$ By using localized virial estimates, we firstly establish general blow-up criteria for non-radial solutions in both L2-critical and L2-supercritical cases. Then, we show existence of normalized standing waves by using the profile decomposition theory in Hs. Combining these results, we study the strong instability of normalized standing waves. Our obtained results greatly improve earlier results.

Stable standing waves for the two-dimensional Klein–Gordon–Schrödinger system

2010 ◽  
Vol 140 (5) ◽  
pp. 1011-1039 ◽  
Author(s):  
Hiroaki Kikuchi
Keyword(s):  
General Theory ◽  
Perturbation Method ◽  
Ground State ◽  
Standing Waves ◽  
Orbital Stability ◽  
Two Dimensional ◽  
Spatial Dimensions ◽  
Klein Gordon ◽  
Linearized Operator ◽  
Schrödinger System

AbstractWe study the orbital stability of standing waves for the Klein–Gordon–Schrödinger system in two spatial dimensions. It is proved that the standing wave is stable if the frequency is sufficiently small. To prove this, we obtain the uniqueness of ground state and investigate the spectrum of the appropriate linearized operator by using the perturbation method developed by Genoud and Stuart and Lin and Wei. Then we apply to our system the general theory of Grillakis, Shatah and Strauss.

scholarly journals Standing Waves for Nonautonomous Klein-Gordon-Maxwell Systems

2019 ◽  
Vol 26 (3) ◽  
pp. 443-454
Author(s):  
Monica Lazzo ◽  
Lorenzo Pisani
Keyword(s):  
Standing Waves ◽  
Klein Gordon

On the Orbital Stability of Standing-Wave Solutions to a Coupled Non-Linear Klein-Gordon Equation

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Daniele Garrisi
Keyword(s):  
Standing Wave ◽  
Ground State ◽  
Gordon Equation ◽  
Standing Waves ◽  
Orbital Stability ◽  
Wave Solutions ◽  
Non Linear ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractWe show the existence of standing-wave solutions to a coupled non-linear Klein-Gordon equation. Our solutions are obtained as minimizers of the energy under a two-charges constraint. We prove that the ground state is stable and that standing-waves are orbitally stable under a non-degeneracy assumption.

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