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Bull. Korean Math. Soc. 2018; 55(4): 1161-1178
Online first article March 27, 2018 Printed July 31, 2018
https://doi.org/10.4134/BKMS.b170634
Copyright © The Korean Mathematical Society.
Global solutions for a class of nonlinear sixth-order wave equation
Ying Wang
University of Electronic Science and Technology of China
In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.
Keywords: Cauchy problem, sixth-order wave equation, blow-up, existence of global solution
MSC numbers: 35L60, 35K55, 35Q80
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