Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition

This paper concerns the polynomial decay of the dissipative wave equation subject to Kinetic boundary condition and non-neglected density in the square. After reformulating this problem into an abstract Cauchy problem, we show the existence and uniqueness of the solution. Then, by analyzing a family...

Full description

Saved in:
Bibliographic Details
Published inActa applicandae mathematicae Vol. 191; no. 1; p. 1
Main Authors Laoubi, K., Seba, D.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2024
Springer Nature B.V
Subjects
Applications of Mathematics
Boundary conditions
Calculus of Variations and Optimal Control; Optimization
Cauchy problems
Computational Mathematics and Numerical Analysis
Decay rate
Eigenvalues
Energy
Existence theorems
Hilbert space
Mathematics
Mathematics and Statistics
Partial Differential Equations
Polynomials
Probability Theory and Stochastic Processes
Uniqueness theorems
Wave equations
Stabilization
35B35
Eigenvalues
Kinetic boundary condition
35L05
35B40
Spectrum
Online AccessGet full text
ISSN0167-8019
1572-9036
DOI10.1007/s10440-024-00650-5

Cover

More Information
Summary:This paper concerns the polynomial decay of the dissipative wave equation subject to Kinetic boundary condition and non-neglected density in the square. After reformulating this problem into an abstract Cauchy problem, we show the existence and uniqueness of the solution. Then, by analyzing a family of eigenvalues of the corresponding operator, we prove that the rate of energy decay decreases in a polynomial way.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-024-00650-5