This paper is concerned with the study of a transmission problem of viscoelastic waves with hereditary memory, establishing the existence, uniqueness and exponential stability for the solutions of this problem. The proof of the stabilization result combines energy estimates and results due to Gérard (Commun Partial Differ Equ 16:1761–1794 (1991)) on microlocal defect measures.

中文翻译：

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粘弹性波动方程传递问题的指数稳定性

本文关注具有遗传记忆的粘弹性波传播问题的研究，建立了该问题解的存在性，唯一性和指数稳定性。稳定结果的证明结合了能量估计值和Gérard的结果（Commun Partial Differ Equ Equ 16：1761–1794（1991）），涉及微局部缺陷测量。