Uniform stability of transmission of wave-plate equations with source on Riemannian manifold

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Hao, Jianghao¹  Wang, Peipei¹ 

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

关键词: Explicit decay rates;    Riemannian manifold;    Transmission system;    Nonlinear boundary feedbacks;   

DOI  :  10.1016/j.jde.2019.11.048

来源: Elsevier

【 摘 要 】

This paper is concerned with the semilinear transmission of wave-plate system with source term on Riemannian manifold. We prove the existence of weak solutions by using Faedo-Galerkin's method. Furthermore, by introducing nonlinear boundary feedbacks acting only on plate, we establish the explicit and general decay rates of the system. Our proofs are based on the geometric multiplier method and the Riemannian geometry method. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free