Stability of coupled wave equations with variable coefficients, localised Kelvin–Voigt damping and time delay

We consider the stabilization of two weakly dissipative wave equations with variable coefficients, localized Kelvin–Voigt damping, mixed boundary condition and time delay. The well posedness is obtained by the semigroup method. Using a unique continuation result, we show that the system is strongly...

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Bibliographic Details
Published in:Semigroup forum 2024-10, Vol.109 (2), p.390-423
Main Authors: Herbadji, Houssem, Khemmoudj, Ammar
Format: Article
Language:English
Subjects:
Algebra
Boundary conditions
Damping
Decay rate
Mathematics
Mathematics and Statistics
Polynomials
Research Article
Time lag
Wave equations
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Summary:We consider the stabilization of two weakly dissipative wave equations with variable coefficients, localized Kelvin–Voigt damping, mixed boundary condition and time delay. The well posedness is obtained by the semigroup method. Using a unique continuation result, we show that the system is strongly stable. Then, we show that the system is not exponentially stable. Finally, using a frequency domain approach combined with multiplier method, we establish a polynomial energy decay rate for the undelayed system. Then, we prove that the system with delay has the same decay rate.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-024-10453-7