Decay estimate and asymptotic profile for a plate equation with memory

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Liu, Yongqin¹  Ueda, Yoshihiro² 

[1] North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China

[2] Kobe Univ, Fac Maritime Sci, Kobe, Hyogo 6580022, Japan

关键词: Asymptotic profile;    Decay estimate;    Plate equation;    Memory effect;    Regularity-loss type;   

DOI  :  10.1016/j.jde.2019.09.007

来源: Elsevier

【 摘 要 】

In this paper, the initial value problem for a plate equation with a memory is considered. Under weaker assumptions on the memory function, we obtain the decay estimates of solutions which is of the regularity-loss type by applying the energy method in Fourier space. Moreover, if the memory kernel is an exponential function, we derive the large-time behavior and asymptotic profile of solutions in the one-dimensional space by virtue of the technique of spectral analysis. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free