A note on the non-existence of global solutions of initial boundary value problems for the Boussinesq equation \(u_{tt}=3u_{xxxx}+u_{xx}- 12(u^ 2)_{xx}\)
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Publication:1074762
DOI10.1016/0022-247X(85)90365-8zbMath0591.35010MaRDI QIDQ1074762
Levine, Howard A., Sleeman, Brian D.
Publication date: 1985
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Ill-posed problems for PDEs (35R25) Blow-up in context of PDEs (35B44)
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Blow-up of solutions for improved Boussinesq type equation ⋮ Longtime dynamics of Boussinesq type equations with fractional damping ⋮ Longtime dynamics of the damped Boussinesq equation ⋮ Refined long time existence of the Boussinesq equation with large initial data in \(\mathbb{R}^n\) ⋮ Blowup of solutions for the bad Boussinesq-type equation. ⋮ The asymptotic solution of the initial boundary value problem to a generalized Boussinesq equation ⋮ Periodic wave solutions and solitary wave solutions of generalized modified Boussinesq equation and evolution relationship between both solutions ⋮ Cauchy problem for the multi-dimensional Boussinesq type equation ⋮ Exact solitary-wave solutions and periodic wave solutions for generalized modified Boussinesq equation and the effect of wave velocity on wave shape ⋮ Existence and blow-up of solution of Cauchy problem for the generalized damped multidimensional Boussinesq equation ⋮ Initial and boundary value problems for a class of nonlinear metaparabolic equations ⋮ On the spatially two-dimensional Boussinesq equation in a circular domain ⋮ Cauchy problem for a higher order generalized Boussinesq-type equation with hydrodynamical damped term ⋮ Global existence and asymptotic behaviour of solutions for the generalized Boussinesq equation ⋮ Global Existence and Decay for Solutions to the “Bad” Boussinesq Equation in Two Space Dimensions ⋮ On local existence of solutions of initial boundary value problems for the ``bad Boussinesq-type equation
Cites Work
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- Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics: The method of unbounded Fourier coefficients
- Blow-up theorems for nonlinear wave equations
- Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
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