Uniform Stabilization for the Semi-linear Wave Equation with Nonlinear Kelvin–Voigt Damping

This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin–Voigt type which is distributed around a neighborhood of the boundary and the second is a frictional damping de...

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 90; no. 2; p. 45
Main Authors Ammari, Kaïs, Cavalcanti, Marcelo M., Mansouri, Sabeur
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2024
Springer Nature B.V
Subjects
Applied mathematics
Calculus of Variations and Optimal Control; Optimization
Control
Damping
Decay rate
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Neighborhoods
Numerical and Computational Physics
Optimization
Simulation
Systems Theory
Theoretical
Viscoelasticity
Wave equations
Uniform stabilization
Nonlinear Kelvin–Voigt damping
Semilinear wave equation
Viscoelastic feedback
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Summary:This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin–Voigt type which is distributed around a neighborhood of the boundary and the second is a frictional damping depending in the first one. We show uniform decay rate results of the corresponding energy for all initial data taken in bounded sets of finite energy phase-space. The proof is based on obtaining an observability inequality which combines unique continuation properties and the tools of the Microlocal Analysis Theory
Bibliography:ObjectType-Article-1
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-024-10186-7