Potential well method for Cauchy problem of generalized double dispersion equations
From MaRDI portal
Publication:2473968
DOI10.1016/j.jmaa.2007.05.076zbMath1140.35011OpenAlexW2033882306MaRDI QIDQ2473968
Publication date: 5 March 2008
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.2007.05.076
Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Initial value problems for higher-order hyperbolic equations (35L30) Higher-order nonlinear hyperbolic equations (35L75)
Related Items
Global existence and nonexistence of solution for Cauchy problem of multidimensional double dispersion equations ⋮ Global existence of solution for Cauchy problem of multidimensional generalized double dispersion equations ⋮ On potential wells to a semilinear hyperbolic equation with damping and conical singularity ⋮ Instability and stability properties of traveling waves for the double dispersion equation ⋮ Global well-posedness for nonlinear fourth-order Schrödinger equations ⋮ The initial-boundary value problem for the generalized double dispersion equation ⋮ Degenerate Kirchhoff-type hyperbolic problems involving the fractional Laplacian ⋮ Global existence, finite time blow-up, and vacuum isolating phenomenon for a class of thin-film equation ⋮ Degenerate Kirchhoff-type diffusion problems involving the fractional \(p\)-Laplacian ⋮ High energy blow up for two-dimensional generalized exponential-type Boussinesq equation ⋮ Global existence, blow-up and optimal decay for a nonlinear viscoelastic equation with nonlinear damping and source term ⋮ Travelling wave solutions for a generalized double dispersion equation ⋮ The Cauchy problem for a class of the multidimensional Boussinesq-type equation ⋮ Blow-up in damped abstract nonlinear equations ⋮ A global attractor for the elastic waveguide model in \(\mathbb R^N\) ⋮ Global existence and nonexistence of solution for Cauchy problem of two-dimensional generalized Boussinesq equations ⋮ Global existence, finite time blow-up and vacuum isolating phenomena for semilinear parabolic equation with conical degeneration ⋮ Global existence of solution for Cauchy problem of two-dimensional Boussinesq-type equation ⋮ Global existence, nonexistence, and decay of solutions for a viscoelastic wave equation with nonlinear boundary damping and source terms ⋮ Qualitative analysis for a degenerate Kirchhoff-type diffusion equation involving the fractional \(p\)-Laplacian ⋮ Symmetries and conservation laws for a sixth-order Boussinesq equation ⋮ Global attractor for the generalized double dispersion equation ⋮ Global existence to generalized Boussinesq equation with combined power-type nonlinearities ⋮ Existence and nonexistence of solutions for a generalized Boussinesq equation ⋮ The initial-boundary value problems for a class of sixth order nonlinear wave equation ⋮ Cauchy problem for a higher order generalized Boussinesq-type equation with hydrodynamical damped term ⋮ Unnamed Item ⋮ The initial-boundary value problems for a class of nonlinear wave equations with damping term ⋮ Convergence of Finite Difference Schemes for a Multidimensional Boussinesq Equation ⋮ Well-posedness of solutions for the sixth-order Boussinesq equation with linear strong damping and nonlinear source ⋮ Analysis of a pseudo-parabolic equation by potential wells ⋮ The Cauchy problem for the Rosenau equation ⋮ Global existence and non-existence analyses to a nonlinear Klein-Gordon system with damping terms under positive initial energy ⋮ Exact solutions of a generalized Boussinesq equation ⋮ Global behavior of the solutions to nonlinear Klein-Gordon equation with critical initial energy ⋮ Initial boundary value problem for a class of fourth-order wave equation with viscous damping term ⋮ Degenerate Kirchhoff-type wave problems involving the fractional Laplacian with nonlinear damping and source terms ⋮ Efficient algorithm and convergence analysis of conservative SAV compact difference scheme for Boussinesq paradigm equation ⋮ Global existence of solution for multidimensional generalized double dispersion equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Instability of standing waves for Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions
- Initial boundary value problem of the generalized cubic double dispersion equation
- Dynamics around the ground state of a nonlinear evolution equation
- A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves
- Saddle points and instability of nonlinear hyperbolic equations
- Solitary longitudinal waves in an inhomogeneous nonlinearly elastic rod
- Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equations
- On potential wells and vacuum isolating of solutions for semilinear wave equations
- Existence and asymptotic stability for evolution problems on manifolds with damping and source terms.
- Multidimensional viscoelasticity equations with nonlinear damping and source terms.
- Qualitative analysis of a nonlinear wave equation
- A characterization of global and nonglobal solutions of nonlinear wave and Kirchhoff equations
- Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term
- The dynamics of a nonlinear wave equation
- Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term
- Nonlinear parabolic equations with critical initial conditions \(J(u_0)=d\) or \(I(u_0)=0\)
- On potential wells and applications to semilinear hyperbolic equations and parabolic equations
- Global solutions and finite time blow up for damped semilinear wave equations
- On global solution of nonlinear hyperbolic equations
- Existence and nonexistence of global solutions for nonlinear parabolic equations
- Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow
- Global existence and blow up of solutions for some hyperbolic systems with damping and source terms
- Cauchy problem of the generalized double dispersion equation
- On Global Existence, Asymptotic Stability and Blowing Up of Solutions for Some Degenerate Non-linear Wave Equations of Kirchhoff Type with a Strong Dissipation
- On the standing wave in coupled non-linear Klein-Gordon equations
- Instability and Blow-Up of Solutions to a Generalized Boussinesq Equation
- Some remarks on the wave equations with nonlinear damping and source terms
This page was built for publication: Potential well method for Cauchy problem of generalized double dispersion equations