scholarly journals On Glassey’s conjecture for semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kimitoshi Tsutaya ◽  
Yuta Wakasugi
Keyword(s):  
Nonlinear Wave ◽  
Finite Time ◽  
Wave Equations ◽  
Nonlinear Term ◽  
Blow Up ◽  
Time Derivative ◽  
Upper Bounds ◽  
Nonlinear Wave Equations ◽  
Semilinear Wave Equations

AbstractConsider nonlinear wave equations in the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. We show blow-up in finite time of solutions and upper bounds of the lifespan of blow-up solutions to give the FLRW spacetime version of Glassey’s conjecture for the time derivative nonlinearity. We also show blow-up results for the space derivative nonlinear term.

scholarly journals Existence, Asymptotic Behaviour, and Blow up of Solutions for a Class of Nonlinear Wave Equations with Dissipative and Dispersive Terms

2009 ◽  
Vol 64 (5-6) ◽  
pp. 315-326
Author(s):  
Necat Polat ◽  
Doğan Kaya
Keyword(s):  
Asymptotic Behaviour ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Term ◽  
Blow Up ◽  
Suitable Condition ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Energy ◽  
Nonlinear Wave Equations

Abstract We consider the existence, both locally and globally in time, the asymptotic behaviour, and the blow up of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative and dispersive terms. Under rather mild conditions on the nonlinear term and the initial data we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the solution decays exponentially to zero as t →+∞. Finally, under a suitable condition on the nonlinear term, we prove that the local solutions with negative and nonnegative initial energy blow up in finite time.

scholarly journals Global existence and finite time blow-up in a class of stochastic nonlinear wave equations

2014 ◽  
Vol 8 (3) ◽  
Author(s):  
Rana D Parshad ◽  
Matthew A Beauregard ◽  
Aslan Kasimov ◽  
Belkacem Said-Houari
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Finite Time ◽  
Wave Equations ◽  
Blow Up ◽  
Nonlinear Wave Equations
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