Potential well method for initial boundary value problem of the generalized double dispersion equations

Yacheng Liu; Runzhang Xu

doi:10.3934/cpaa.2008.7.63

Article Contents

2008, Volume 7, Issue 1: 63-81. Doi: 10.3934/cpaa.2008.7.63

This issue Previous Article On the rate of convergence of periodic solutions in perturbed autonomous systems as the perturbation vanishes Next Article A variational argument to finding global solutions of a quasilinear Schrödinger equation

Potential well method for initial boundary value problem of the generalized double dispersion equations

Yacheng Liu¹ and
Runzhang Xu^1,

1.
College of Science, Harbin Engineering University, Harbin, 150001

Received: September 30, 2006

Revised: April 30, 2007

Published: December 2007

Abstract Related Papers Cited by

Abstract

In this paper we study the initial boundary value problem of the generalized double dispersion equations $u_{t t}-u_{x x}-u_{x x t t}+u_{x x x x}=f(u)_{x x}$, where $f(u)$ include convex function as a special case. By introducing a family of potential wells we first prove the invariance of some sets and vacuum isolating of solutions, then we obtain a threshold result of global existence and nonexistence of solutions. Finally we discuss the global existence of solutions for problem with critical initial condition.

Keywords:

Mathematics Subject Classification: Primary: 35M20, 35Q72.

Citation:

Article Metrics

HTML views() PDF downloads(165) Cited by(0)

Potential well method for initial boundary value problem of the generalized double dispersion equations

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Potential well method for initial boundary value problem of the generalized double dispersion equations

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content