Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (1): 155-169.doi: 10.1007/s10473-020-0111-2

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GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

Jiali YU1,2, Yadong SHANG2, Huafei DI2   

  1. 1. School of Science, Dalian Jiaotong University, Dalian 116028, China;
    2. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
  • Received:2018-11-07 Revised:2019-05-09 Online:2020-02-25 Published:2020-04-14
  • Contact: Yadong SHANG E-mail:gzydshang@126.com
  • Supported by:
    This work was supported by the NSF of China (11626070, 11801108), the Scientific Program of Guangdong Provience (2016A030310262), the College Scientific Research Project of Guangzhou City (1201630180), the Program for the Innovation Research Grant for the Postgraduates of Guangzhou University (2017GDJC-D08).

Abstract: This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms
utt - △u - △ut - △utt + ∫0tg(t - s)△u(s)ds + ut|ut|m-2=u|u|p-2
with acoustic boundary conditions. Under some appropriate assumption on relaxation function g and the initial data, we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.

Key words: viscoelastic wave equation, Global nonexistence, Acoustic boundary conditions

CLC Number: 

  • 35L70
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