Global existence and blow-up for the generalized sixth-order Boussinesq equation

2012 ◽  
Vol 75 (11) ◽  
pp. 4325-4338 ◽  
Author(s):  
Amin Esfahani ◽  
Luiz Gustavo Farah ◽  
Hongwei Wang
Keyword(s):  
Global Existence ◽  
Boussinesq Equation ◽  
Blow Up ◽  
Sixth Order

scholarly journals Well-posedness results for a sixth-order logarithmic Boussinesq equation

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 3985-4000
Author(s):  
Erhan Pişkin ◽  
Nazlı Irkıl
Keyword(s):  
Global Existence ◽  
Galerkin Method ◽  
Sobolev Inequality ◽  
Boussinesq Equation ◽  
Blow Up ◽  
Existence Of Solutions ◽  
Sixth Order ◽  
Well Posedness ◽  
Decay Estimates ◽  
Global Existence Of Solutions

The main goal of this paper is to study for a sixth-order logarithmic Boussinesq equation. We obtain several results: Firstly, by using Feado-Galerkin method and a logaritmic Sobolev inequality, we proved global existence of solutions. Later, we proved blow up property in infinity time of solutions. Finally, we showed the decay estimates result of the solutions.

Global existence and blowup of solutions for the multidimensional sixth-order “good” Boussinesq equation

2014 ◽  
Vol 66 (3) ◽  
pp. 955-976 ◽  
Author(s):  
Xu Runzhang ◽  
Yang Yanbing ◽  
Liu Bowei ◽  
Shen Jihong ◽  
Huang Shaobin
Keyword(s):  
Global Existence ◽  
Boussinesq Equation ◽  
Sixth Order ◽  
Blowup Of Solutions

scholarly journals Blow-up for the sixth-order multidimensional generalized Boussinesq equation with arbitrarily high initial energy

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jianghao Hao ◽  
Aiyuan Gao
Keyword(s):  
Cauchy Problem ◽  
Fourier Transform ◽  
Finite Time ◽  
Boussinesq Equation ◽  
Blow Up ◽  
Initial Energy ◽  
Sixth Order ◽  
The Cauchy Problem ◽  
Generalized Boussinesq Equation

AbstractIn this paper, we consider the Cauchy problem for the sixth-order multidimensional generalized Boussinesq equation with double damping terms. By using the improved convexity method combined with Fourier transform, we show the finite time blow-up of solution with arbitrarily high initial energy.

scholarly journals Blow-up phenomena for the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jinxing Liu ◽  
Xiongrui Wang ◽  
Jun Zhou ◽  
Huan Zhang
Keyword(s):  
Lower Bounds ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
Blow Up ◽  
Sixth Order ◽  
Upper And Lower Bounds ◽  
Differential Inequalities ◽  
Nonlinear Source ◽  
Order Dispersion ◽  
Dispersion Term

<p style='text-indent:20px;'>This paper deals with the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source. By using some ordinary differential inequalities, the conditions on finite time blow-up of solutions are given with suitable assumptions on initial values. Moreover, the upper and lower bounds of the blow-up time are also investigated.</p>

Global existence and blow up for damped generalized Boussinesq equation

2017 ◽  
Vol 33 (1) ◽  
pp. 251-262 ◽  
Author(s):  
Run-zhang Xu ◽  
Yong-bing Luo ◽  
Ji-hong Shen ◽  
Shao-bin Huang
Keyword(s):  
Global Existence ◽  
Boussinesq Equation ◽  
Blow Up ◽  
Generalized Boussinesq Equation
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