On the Cauchy problem for the damped Boussinesq equation

zbMath0844.35095MaRDI QIDQ1909704

Vladimir V. Varlamov

Publication date: 24 April 1996

Published in: Differential and Integral Equations (Search for Journal in Brave)

zbMATH Keywords

Cauchy problemBoussinesq equationBurgers equationlarge time asymptoticssmall initial data

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (20)

Global existence and long-time behavior of the initial-boundary value problem for the dissipative Boussinesq equation ⋮ Blow-up and scattering of solution for a generalized Boussinesq equation ⋮ Asymptotics in the critical case for Whitham type equations ⋮ Dispersive estimates and asymptotic behavior for a generalized Boussinesq-type equation ⋮ Influence of dissipation on solitary wave solution to generalized Boussinesq equation ⋮ The asymptotic solution of the initial boundary value problem to a generalized Boussinesq equation ⋮ Symmetry multi-reduction method for partial differential equations with conservation laws ⋮ Instability of the stationary solutions of generalized dissipative Boussinesq equation. ⋮ The Cauchy problem for the dissipative Boussinesq equation ⋮ Global existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation ⋮ Global existence and blow up for damped generalized Boussinesq equation ⋮ Periodic behavior for the parametrically excited Boussinesq equation ⋮ On the spatially two-dimensional Boussinesq equation in a circular domain ⋮ Asymptotic behaviors of solutions to a sixth-order Boussinesq equation with logarithmic nonlinearity ⋮ Inviscid limit for the damped Boussinesq equation ⋮ Decay estimates for a dissipative-dispersive linear semigroup and application to the viscous Boussinesq equation ⋮ Global existence and nonexistence of the initial-boundary value problem for the dissipative Boussinesq equation ⋮ Well-posedness of solutions for the sixth-order Boussinesq equation with linear strong damping and nonlinear source ⋮ Decay and scattering of solutions for a generalized Boussinesq equation ⋮ The Cauchy problem for the nonlinear viscous Boussinesq equation in the \(L^q\) framework

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