Global existence and asymptotic behaviour of solutions for the generalized Boussinesq equation

DOI10.1016/J.NA.2007.12.018zbMath1161.35470OpenAlexW2017879926MaRDI QIDQ2518595

Yu-Zhu Wang

Publication date: 16 January 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.12.018

zbMATH Keywords

global solutiongeneralized Boussinesq equationasymptotic behaviour of solutionlocal solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) A priori estimates in context of PDEs (35B45)

Related Items (16)

Decay estimate of solutions to the sixth order damped Boussinesq equation ⋮ Existence and asymptotic stability of time periodic solutions to the generalized double dispersion equation with periodic external force ⋮ GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO CAHN–HILLIARD EQUATION WITH INERTIAL TERM ⋮ Asymptotic behavior of solutions to the damped nonlinear hyperbolic equation ⋮ The ``good Boussinesq equation: long-time asymptotics ⋮ Global existence and asymptotic behavior of solutions for a semi-linear wave equation ⋮ Large time behavior of solutions to the nonlinear pseudo-parabolic equation ⋮ Global existence and asymptotic behavior of solutions to a class of fourth-order wave equations ⋮ Potential method applied to Boussinesq equation ⋮ Asymptotic behavior of global solutions to the Boussinesq equation in multidimensions ⋮ A class of dissipative wave equations with time-dependent speed and damping ⋮ Existence and asymptotic behavior of solution of Cauchy problem for the damped sixth-order Boussinesq equation ⋮ Initial boundary value problem for generalized logarithmic improved Boussinesq equation ⋮ Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation ⋮ Solitonic solutions for a variable-coefficient variant Boussinesq system in the long gravity waves ⋮ Global existence and asymptotic behavior of solutions to a nonlinear wave equation of fourth-order

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on the non-existence of global solutions of initial boundary value problems for the Boussinesq equation \(u_{tt}=3u_{xxxx}+u_{xx}- 12(u^ 2)_{xx}\)
• The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types
• Global existence of small solutions for a generalized Boussinesq equation
• Decay and scattering of small solutions of a generalized Boussinesq equation
• Small amplitude solutions of the generalized IMBq equation.
• Partial differential equations. 2: Qualitative studies of linear equations
• Blow-up and scattering of solution for a generalized Boussinesq equation
• Cauchy problem of the generalized double dispersion equation
• Global Existence and Asymptotic Stability for a Semilinear Hyperbolic Volterra Equation with Large Initial Data
• Global Existence and Decay for Solutions to the “Bad” Boussinesq Equation in Two Space Dimensions
• Asymptotic behavior of solutions of a generalized Boussinesq type equation
• Global existence and blow‐up of the solutions for the multidimensional generalized Boussinesq equation
• New exact solutions of the Boussinesq equation
• Kawahara dynamics in dispersive media

This page was built for publication: Global existence and asymptotic behaviour of solutions for the generalized Boussinesq equation