Local and global existence of solutions for the Cauchy problem of a generalized Boussinesq equation
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Publication:819707
DOI10.1016/j.jmaa.2005.04.041zbMath1106.35069OpenAlexW2001209637MaRDI QIDQ819707
Publication date: 29 March 2006
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.04.041
PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)
Related Items (25)
Global solution for a generalized Boussinesq equation ⋮ Global existence and exponential growth of solution for the logarithmic Boussinesq-type equation ⋮ Well-posedness of solutions for the dissipative Boussinesq equation with logarithmic nonlinearity ⋮ A non-homogeneous boundary value problem of the sixth order Boussinesq equation in a quarter plane ⋮ Low regularity solutions of non-homogeneous boundary value problems of a higher order Boussinesq equation in a quarter plane ⋮ Global solution to the Cauchy problem for nonlinear three-dimensional thermoelasticity of nonsimple materials ⋮ Low regularity solution of the initial-boundary-value problem for the ``good Boussinesq equation on the half line ⋮ Refined long time existence of the Boussinesq equation with large initial data in \(\mathbb{R}^n\) ⋮ The Cauchy problem for a class of the multidimensional Boussinesq-type equation ⋮ On global solutions for the Cauchy problem of a Boussinesq-type equation ⋮ Blow-up for generalized Boussinesq equation with double damping terms ⋮ Wellposedness of the sixth order Boussinesq equation with non-homogeneous boundary values on a bounded domain ⋮ The initial-boundary value problem for the ``good Boussinesq equation on the bounded domain ⋮ Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation ⋮ The Cauchy problem for the dissipative Boussinesq equation ⋮ The initial-boundary-value problem for the ``good Boussinesq equation on the half line ⋮ Global existence and blow up for damped generalized Boussinesq equation ⋮ Existence and nonexistence of solutions for a generalized Boussinesq equation ⋮ Asymptotic behaviors of solutions to a sixth-order Boussinesq equation with logarithmic nonlinearity ⋮ Decay estimates for a dissipative-dispersive linear semigroup and application to the viscous Boussinesq equation ⋮ Well-posedness of solutions for the sixth-order Boussinesq equation with linear strong damping and nonlinear source ⋮ Global well-posedness for the Cauchy problem of generalized Boussinesq equations in the control problem regarding initial data ⋮ Blow-up phenomena for the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source ⋮ Cauchy problem of generalized Boussinesq equation with combined power-type nonlinearities ⋮ The Cauchy problem for the nonlinear viscous Boussinesq equation in the \(L^q\) framework
Cites Work
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- Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation
- Global existence of small solutions for a generalized Boussinesq equation
- Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
- The cauchy problem for the critical nonlinear Schrödinger equation in Hs
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- On the Cauchy Problem for the Generalized Korteweg-de Vries Equation
- Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory
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