Exponential stability result for the wave equation with Kelvin–Voigt damping and past history subject to Wentzell boundary condition and delay term

In this paper, we present an analysis of stability of solutions corresponding to a variable coefficient's wave equation subject to a locally Kelvin–Voigt damping and distributed effect driven by a nonnegative function b(x)≥0$$ b(x)\ge 0 $$ with dynamic Wentzell boundary conditions and delay ter...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 47; no. 3; pp. 1546 - 1576
Main Authors Kechiche, Dounya, Khemmoudj, Ammar, Medjden, Mohammed
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.02.2024
Subjects
Boundary conditions
Damping
Decay
Delay
delay term
frequency domain approach method
Kelvin–Voigt damping
past history term
Stability analysis
wave equation
Wave equations
WBC
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Summary:In this paper, we present an analysis of stability of solutions corresponding to a variable coefficient's wave equation subject to a locally Kelvin–Voigt damping and distributed effect driven by a nonnegative function b(x)≥0$$ b(x)\ge 0 $$ with dynamic Wentzell boundary conditions and delay term. By using frequency domain approach method, we show that under a suitable assumption between the internal damping function c$$ c $$ and the boundary delay feedback, considering some geometrical assumptions on the boundary of Ω$$ \Omega $$, supposing that the relaxation function h$$ h $$ decay exponentially to zero, that the energies of the problem decay exponentially to zero.
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content type line 14
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9708