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Open Access Research

Global existence of solutions for 1-D nonlinear wave equation of sixth order at high initial energy level

Jihong Shen2, Yanbing Yang1 and Runzhang Xu12*

Author Affiliations

1 College of Automation, Harbin Engineering University, Harbin, 150001, People’s Republic of China

2 College of Science, Harbin Engineering University, Harbin, 150001, People’s Republic of China

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Boundary Value Problems 2014, 2014:31  doi:10.1186/1687-2770-2014-31

Published: 4 February 2014

Abstract

This paper considers the Cauchy problem of solutions for a class of sixth order 1-D nonlinear wave equations at high initial energy level. By introducing a new stable set we derive the result that certain solutions with arbitrarily positive initial energy exist globally.

Keywords:
Cauchy problem; sixth order wave equation; global existence; arbitrarily positive initial energy; potential well