The Limit Behavior of Solutions for the Cauchy Problem of the Sixth-Order Boussinesq Equation

2021 ◽  
Vol 176 (1) ◽  
Author(s):  
Hongwei Wang ◽  
Amin Esfahani
Keyword(s):  
Cauchy Problem ◽  
Boussinesq Equation ◽  
Limit Behavior ◽  
Sixth Order ◽  
The Cauchy Problem

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.

On the Cauchy problem for one dimension generalized Boussinesq equation

2015 ◽  
Vol 26 (03) ◽  
pp. 1550023 ◽  
Author(s):  
Yinxia Wang
Keyword(s):  
Cauchy Problem ◽  
Boussinesq Equation ◽  
Nonlinear Approximation ◽  
Global Solutions ◽  
One Dimension ◽  
Diffusion Waves ◽  
Self Similar Solution ◽  
The Cauchy Problem ◽  
Nonlinear Diffusion Waves ◽  
Generalized Boussinesq Equation

In this paper, we study the Cauchy problem for one dimension generalized damped Boussinesq equation. First, global existence and decay estimate of solutions to this problem are established. Second, according to the detail analysis for solution operator the generalized damped Boussinesq equation, the nonlinear approximation to global solutions is established. Finally, we prove that the global solution u to our problem is asymptotic to the superposition of nonlinear diffusion waves expressed in terms of the self-similar solution of the viscous Burgers equation as time tends to infinity.

scholarly journals Global Existence and Asymptotic Behavior of Solutions to the Generalized Damped Boussinesq Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yinxia Wang ◽  
Hengjun Zhao
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Global Existence ◽  
Decay Estimate ◽  
Boussinesq Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
Linear Solution ◽  
Optimal Decay ◽  
The Cauchy Problem

We investigate the Cauchy problem for the generalized damped Boussinesq equation. Under small condition on the initial value, we prove the global existence and optimal decay estimate of solutions for all space dimensionsn≥1. Moreover, whenn≥2, we show that the solution can be approximated by the linear solution as time tends to infinity.

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