Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations.

Xiuyan Peng; Yi Niu

doi:10.4208/jpde.v30.n2.1

Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations.

Authors

Xiuyan Peng College of Automation, Harbin Engineering University, Harbin 150001, China
Yi Niu College of Automation, Harbin Engineering University, Harbin 150001, China

DOI:

https://doi.org/10.4208/jpde.v30.n2.1

Keywords:

Generalized Boussinesq equations;Cauchy problem;global existence;nonexistence

Abstract

This paper consider the Cauchy problemfor a class of 1Dgeneralized Boussinesq equations u_tt-u_xx-u_xxtt+u_xxxx+u_xxxxtt= f(u)_xx. By utilizing the potential well method and giving some conditions on f(u), we obtain the invariance of some sets and obtain the threshold result of global existence and nonexistence of solutions.

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Published

2017-05-02

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Issue

Vol. 30 No. 2 (2017)

Section

Articles

How to Cite

Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations. (2017). Journal of Partial Differential Equations, 30(2), 95-110. https://doi.org/10.4208/jpde.v30.n2.1