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Title: Around certain critical cases in stability studies in hydraulic engineering (English)
Author: Rasvan, Vladimir
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 59
Issue: 1
Year: 2023
Pages: 109-116
Summary lang: English
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Category: math
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Summary: It is considered the mathematical model of a benchmark hydroelectric power plant containing a water reservoir (lake), two water conduits (the tunnel and the turbine penstock), the surge tank and the hydraulic turbine; all distributed (Darcy-Weisbach) and local hydraulic losses are neglected,the only energy dissipator remains the throttling of the surge tank. Exponential stability would require asymptotic stability of the difference operator associated to the model. However in this case this stability is “fragile” i.e. it holds only for a rational ratio of the two delays, with odd numerator and denominator also. Otherwise this stability is critical (non-asymptotic and displaying an oscillatory mode). (English)
Keyword: neutral functional differential equations
Keyword: energy Lyapunov functional
Keyword: asymptotic stability
Keyword: water hammer
MSC: 34D20
MSC: 34K20
MSC: 34K40
MSC: 35L50
idZBL: Zbl 07675579
idMR: MR4563021
DOI: 10.5817/AM2023-1-109
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Date available: 2023-02-22T14:33:26Z
Last updated: 2023-05-04
Stable URL: http://hdl.handle.net/10338.dmlcz/151555
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Reference: [10] Răsvan, V.: Critical cases in neutral functional differential equations, arising from hydraulic engineering.Opuscula Math. 42 (4) (2022), 605–633. MR 4449109, 10.7494/OpMath.2022.42.4.605
Reference: [11] Răsvan, V.: Stability results for the functional differential equations associated to water hammer in hydraulics.Electron. J. Qual. Theory Differ. Equ. 19 (2022), 1–32. MR 4417616, 10.14232/ejqtde.2022.1.19
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