Cauchy problem of generalized Boussinesq equation with combined power-type nonlinearities

DOI10.1002/MMA.1536zbMath1236.35125OpenAlexW2061992580MaRDI QIDQ3106283

Xu Runzhang

Publication date: 20 December 2011

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.1536

zbMATH Keywords

Cauchy problemglobal solutionblow upgeneralized Boussinesq equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Weak solutions to PDEs (35D30) Blow-up in context of PDEs (35B44)

Related Items (12)

Global solutions of wave equations with multiple nonlinear source terms under acoustic boundary conditions ⋮ Well-posedness of solutions for the dissipative Boussinesq equation with logarithmic nonlinearity ⋮ High energy blow up for two-dimensional generalized exponential-type Boussinesq equation ⋮ On global solutions for the Cauchy problem of a Boussinesq-type equation ⋮ Global existence to generalized Boussinesq equation with combined power-type nonlinearities ⋮ Asymptotic behaviors of solutions to a sixth-order Boussinesq equation with logarithmic nonlinearity ⋮ Well-posedness of solutions for the sixth-order Boussinesq equation with linear strong damping and nonlinear source ⋮ Nonexistence of global solutions to new ordinary differential inequality and applications to nonlineardispersive equations ⋮ Initial boundary value problem for generalized logarithmic improved Boussinesq equation ⋮ Blow-up phenomena for the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source ⋮ Global behavior of the solutions to nonlinear Klein-Gordon equation with critical initial energy ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Instability of solitary waves for generalized Boussinesq equations
• Local and global existence of solutions for the Cauchy problem of a generalized Boussinesq equation
• Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation
• Wave equations and reaction-diffusion equations with several nonlinear source terms
• On the Cauchy problem for a generalized Boussinesq equation
• 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
• Improved blow-up of solutions of a generalized Boussinesq equation
• Wave equations and reaction-diffusion equations with several nonlinear source terms of different sign
• Instability and Blow-Up of Solutions to a Generalized Boussinesq Equation
• The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities
• Solutions of the Boussinesq equation on a periodic domain

This page was built for publication: Cauchy problem of generalized Boussinesq equation with combined power-type nonlinearities