The initial-boundary value problems for a class of sixth order nonlinear wave equation

Runzhang Xu; Mingyou Zhang; Shaohua Chen; Yanbing Yang; Jihong Shen

doi:10.3934/dcds.2017244

Article Contents

2017, Volume 37, Issue 11: 5631-5649. Doi: 10.3934/dcds.2017244

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The initial-boundary value problems for a class of sixth order nonlinear wave equation

1.
College of Science, Harbin Engineering University, Heilongjiang, Harbin 150001, China
2.
The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
3.
College of Automation, Harbin Engineering University, Heilongjiang, Harbin 150001, China
4.
Department of Mathematics, Cape Breton University, Sydney, NS, B1P 6L2, Canada

* Corresponding author: Runzhang Xu, xurunzh@163.com.
* Corresponding author: Runzhang Xu, xurunzh@163.com.

Received: February 28, 2017

Revised: May 31, 2017

Published: October 2017

This work was supported by the National Natural Science Foundation of China (11471087), the China Postdoctoral Science Foundation(2013M540270), the Fundamental Research Funds for the Central Universities

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Abstract

This paper considers the initial boundary value problem of solutions for a class of sixth order 1-D nonlinear wave equations. We discuss the probabilities of the existence and nonexistence of global solutions and give some sufficient conditions for the global and non-global existence of solutions at three different initial energy levels, i.e., sub-critical level, critical level and sup-critical level.

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Mathematics Subject Classification: Primary: 35L35, 35A01; Secondary: 35B44, 35L75.

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