Decay Properties for Transmission System with Infinite Memory and Distributed Delay

We consider a damped transmission problem in a bounded domain where the damping is effective in a neighborhood of a suitable subset of the boundary. Using the semigroup approach together with Hille–Yosida theorem, we prove the existence and uniqueness of global solution. Under suitable assumption on...

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Bibliographic Details
Published inFractal and fractional Vol. 8; no. 2; p. 94
Main Authors Saber, Hicham, Braik, Abdelkader, Bahri, Noureddine, Beniani, Abderrahmane, Alraqad, Tariq, Jawarneh, Yousef, Zennir, Khaled
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2024
Subjects
Damping
Distributed memory
Existence theorems
exponential stability
Hilbert space
internal distributed delay
Lyapunov functions
multiplier method
transmission problem
well-posedness
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Summary:We consider a damped transmission problem in a bounded domain where the damping is effective in a neighborhood of a suitable subset of the boundary. Using the semigroup approach together with Hille–Yosida theorem, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8020094