scholarly journals Blow-up and strong instability of standing waves for the NLS-δ equation on a star graph

2020 ◽  
Vol 196 ◽  
pp. 111753
Author(s):  
Nataliia Goloshchapova ◽  
Masahito Ohta
Keyword(s):  
Blow Up ◽  
Standing Waves ◽  
Star Graph ◽  
Strong Instability

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.

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 Variational properties and orbital stability of standing waves for NLS equation on a star graph

2014 ◽  
Vol 257 (10) ◽  
pp. 3738-3777 ◽  
Author(s):  
Riccardo Adami ◽  
Claudio Cacciapuoti ◽  
Domenico Finco ◽  
Diego Noja
Keyword(s):  
Standing Waves ◽  
Orbital Stability ◽  
Star Graph ◽  
Nls Equation

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
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