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Note on stability of an abstract coupled hyperbolic-parabolic system: singular case
Kaïs Ammari, Farhat Shel, Zhuangyi Liu
In this paper we try to complete the stability analysis for an abstract system of coupled hyperbolic and parabolic equations $$ \left\{ \begin{array}{lll} \ds u_{tt} + Au - A^αw =…
Stabilisation of the generalised Rao-Nakra beam by partial viscous damping
Mohammad Akil, Zhuangyi Liu
In this paper, we consider the stabilization of the generalized Rao-Nakra beam equation, which consists of four wave equations for the longitudinal displacements and the shear angl…
Stability of the wave equations on a tree with local Kelvin-Voigt damping
Kaïs Ammari, Zhuangyi Liu, Farhat Shel
In this paper we study the stability problem of a tree of elastic strings with local Kelvin-Voigt damping on some of the edges. Under the compatibility condition of displacement an…
Regularity Analysis for an Abstract System of Coupled Hyperbolic and Parabolic Equations
Jianghao Hao, Zhuangyi Liu, Jiongmin Yong
In this paper, we provide a complete regularity analysis for an abstract system of coupled hyperbolic and parabolic equations in a complex Hilbert space. We are able to decompose t…