Global Existence and Asymptotic Behavior of Solutions to the Generalized Damped Boussinesq Equation
Yinxia Wang,Hengjun Zhao +1 more
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In this article, the authors investigated the Cauchy problem for the generalized damped Boussinesq equation and showed that the solution can be approximated by the linear solution as time tends to infinity.Abstract:
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 dimensions . Moreover, when , we show that the solution can be approximated by the linear solution as time tends to infinity.read more
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On the Cauchy problem for one dimension generalized Boussinesq equation
TL;DR: In this article, the Cauchy problem for one dimension generalized damped Boussinesq equation is studied and the global solution u to u 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.
Journal ArticleDOI
Large‐time behavior of solutions to the Rosenau equation with damped term
Yin-Xia Wang,Gaihong Feng +1 more
TL;DR: In this article, the authors considered the initial value problem for the Rosenau equation with damped term and showed that the global solutions may be approximated by the superposition of nonlinear diffusion wave for n = 1.
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Well-Posedness of Solutions for the Sixth-Order Boussinesq Equation with Linear Strong Damping and Nonlinear Source
Jun Zhou,Huan Zhang +1 more
TL;DR: In this article, the authors studied the local well-posedness of the solutions of the Boussinesq equation with dispersive, linear strong damping and nonlinear source by using potential well methods.
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Asymptotic Behavior of Global Solutions to the Boussinesq Equation in Multidimensions
Yu-Zhu Wang,Qingnian Zhang +1 more
TL;DR: In this paper, the Cauchy problem for the Boussinesq equation in multidimensions is investigated and the asymptotic behavior of the global solutions provided that the initial data are suitably small.
References
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TL;DR: A survey of the properties of soliton-type solutions to non-linear wave equations appearing in various fields of physics is given in this paper, where the results of computer experiments on the dynamics of the formation and interaction (in one-space-dimensional geometry) of solit-type objects are presented at length.
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Lp-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application
TL;DR: In this article, the authors considered the Cauchy problem in 3D space for the linear damped wave equation and the corresponding parabolic equation, and obtained the Lp−Lq estimates of the difference of each solution, which represent the assertion precisely.
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