Opuscula Math. 39, no. 2 (2019), 297-313

Opuscula Mathematica

Global well-posedness of a class of fourth-order strongly damped nonlinear wave equations

Yang Yanbing
Md Salik Ahmed
Qin Lanlan
Xu Runzhang

Abstract. Global well-posedness and finite time blow up issues for some strongly damped nonlinear wave equation are investigated in the present paper. For subcritical initial energy by employing the concavity method we show a finite time blow up result of the solution. And for critical initial energy we present the global existence, asymptotic behavior and finite time blow up of the solution in the framework of the potential well. Further for supercritical initial energy we give a sufficient condition on the initial data such that the solution blows up in finite time.

Keywords: fourth-order nonlinear wave equation, strong damping, blow up, global existence.

Mathematics Subject Classification: 35B44, 35L35, 35L05.

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  • Yang Yanbing
  • Harbin Engineering University, College of Science, 150001, People's Republic of China
  • Md Salik Ahmed
  • Harbin Engineering University, College of Science, 150001, People's Republic of China
  • Qin Lanlan
  • Harbin Engineering University, College of Science, 150001, People's Republic of China
  • Communicated by Marius Ghergu.
  • Received: 2018-03-07.
  • Accepted: 2018-11-03.
  • Published online: 2018-12-07.
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Cite this article as:
Yang Yanbing, Md Salik Ahmed, Qin Lanlan, Xu Runzhang, Global well-posedness of a class of fourth-order strongly damped nonlinear wave equations, Opuscula Math. 39, no. 2 (2019), 297-313, https://doi.org/10.7494/OpMath.2019.39.2.297

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