대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제55권4호
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  • Pages.1161-1178
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  • 2018
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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GLOBAL SOLUTIONS FOR A CLASS OF NONLINEAR SIXTH-ORDER WAVE EQUATION

  • Wang, Ying (School of Mathematical Sciences University of Electronic Science and Technology of China)
  • 투고 : 2017.07.19
  • 심사 : 2017.12.29
  • 발행 : 2018.07.31
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초록

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.

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참고문헌

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