Decay and scattering of solutions for a generalized Boussinesq equation

DOI10.1016/J.JDE.2009.07.022zbMath1179.35252OpenAlexW1966837657MaRDI QIDQ1032881

Ying Wang, Yong-Hong Wu, Chun-Lai Mu

Publication date: 5 November 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.07.022

zbMATH Keywords

scatteringBoussinesq equationdecay

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)

Related Items (9)

Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation ⋮ Stability analysis of solutions for the sixth-order nonlinear Boussinesq water wave equations in two-dimensions and its applications ⋮ Global existence and pointwise estimates of solutions for the multidimensional generalized Boussinesq-type equation ⋮ Decay and scattering of small solutions for Rosenau equations ⋮ Upper and lower bounds of time decay rate of solutions to a class of incompressible third grade fluid equations ⋮ Global attractors for the semilinear beam equation with localized viscosity ⋮ Asymptotic behavior for the singularly perturbed damped Boussinesq equation ⋮ Asymptotic behavior for the damped Boussinesq equation with critical nonlinearity ⋮ Global existence and blowup of solutions for the multidimensional sixth-order ``good Boussinesq equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Instability of solitary waves for generalized Boussinesq equations
• Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation
• 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
• On the initial-boundary value problem for the damped Boussinesq equation
• The Cauchy problem for the generalized IMBq equation in \(W^{s,p}(\mathbb R^n)\).
• Small amplitude solutions of the generalized IMBq equation.
• On the Cauchy problem for the damped Boussinesq equation
• Blow-up and scattering of solution for a generalized Boussinesq equation
• The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation
• On a Growing Mode of the Boussinesq Equation
• Soliton and antisoliton interactions in the ‘‘good’’ Boussinesq equation
• On the damped Boussinesq equation in a circle
• Instability and Blow-Up of Solutions to a Generalized Boussinesq Equation
• 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
• Eigenfunction expansion method and the long-time asymptotics for the damped Boussinesq equation

This page was built for publication: Decay and scattering of solutions for a generalized Boussinesq equation