On the blowup of solutions of a Schrödinger equation with an inhomogeneous damping coefficient

2014 ◽  
Vol 16 (03) ◽  
pp. 1350036 ◽  
Author(s):  
João-Paulo Dias ◽  
Mário Figueira
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Damping Coefficient ◽  
Blowup Of Solutions ◽  
Blowing Up ◽  
The Cauchy Problem ◽  
Local Solutions ◽  
Blowup Result ◽  
Suitable Initial Data ◽  
Blowing Up Solutions

We consider the Cauchy problem for the nonlinear self-focusing Schrödinger equation in ℝNwith an inhomogeneous smooth damping coefficient and we prove, for suitable initial data, and in the spirit of the seminal work of R. Glassey, a blowup result for the corresponding local solutions. We also give some lower bound estimates for the blowing-up solutions.

scholarly journals Finite speed of disturbance for the nonlinear Schrödinger equation

2018 ◽  
Vol 149 (6) ◽  
pp. 1405-1419
Author(s):  
Simão Correia
Keyword(s):  
Initial Data ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Finite Speed Of Propagation ◽  
Finite Speed ◽  
Nonlinear Schrödinger ◽  
The Cauchy Problem ◽  
Whole Space

AbstractWe consider the Cauchy problem for the nonlinear Schrödinger equation on the whole space. After introducing a weaker concept of finite speed of propagation, we show that the concatenation of initial data gives rise to solutions whose time of existence increases as one translates one of the initial data. Moreover, we show that, given global decaying solutions with initial data u0, v0, if |y| is large, then the concatenated initial data u0 + v0(· − y) gives rise to globally decaying solutions.

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