Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1428-1444.

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General Decay for the Transmission Problem of Viscoelastic Waves with not Necessarily Decreasing Kernel

Zhiqing Liu1(),Zhongbo Fang2,*()   

  1. 1 School of Mathematics and Physics, Qingdao University of Science and Technology, Shandong Qingdao 266061
    2 School of Mathematical Sciences, Ocean University of China, Shandong Qingdao 266100
  • Received:2020-01-08 Online:2021-10-26 Published:2021-10-08
  • Contact: Zhongbo Fang;
  • Supported by:
    the NSF of Shandong Province(ZR2019MA072);the Fundamental Research Funds for the Central Universities(201964008)


In this paper, we are concerned with the asymptotic behavior for a transmission problem of viscoelastic waves with not necessarily decreasing kernel. We construct a new Lyapunov functional to derive the general decay estimate. Meanwhile, we present an example to illustrate that the decay rate we obtained includes exponential, algebraic and logarithmic decay etc.

Key words: Transmission problem, Not necessarily decreasing kernel, General decay

CLC Number: 

  • O175