Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions

In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order 1 < α &l...

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Bibliographic Details
Published in:The Journal of geometric analysis 2023-02, Vol.33 (2), Article 45
Main Authors: Ge, Hui, Zhang, Zhifei
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Damping
Decay rate
Differential Geometric PDE Control
Differential Geometry
Dynamical Systems and Ergodic Theory
Feedback control
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
Polynomials
Riemann manifold
Shape Optimization and Applications
Wave equations
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Summary:In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order 1 < α < 2 . Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-022-01100-0