Existence and stability of periodic solution related to valveless pumping
type: Item
instance of: scholarly article
title: Existence and stability of periodic solution related to valveless pumping
zbMATH Open document ID: 1427.34051
DOI: 10.1155/2018/3982432
author: M. Sága
author: Carlos Llopis-Albert
author: B. Dorociaková
author: Mária Michalková
author: R. Olach
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: Valveless pumping, also known as Liebau effect, can be described as the unidirectional flow of liquid in a system without valves that is caused by the asymmetry of placing of the periodically working pump. Recently, the research in this field has been reevoked, partially due to its possible application in nanotechnologies. In this paper, a configuration of one pipe and one tank is considered from the mathematical point of view. Qualitative properties of a class of nonlinear differential equations that model the assumed system configuration are investigated. New sufficient conditions for the existence of positive \(T\)-periodic solutions are given. Correspondingly, exponential stability of periodic solution is treated. Presented results are new. They extend and complement earlier ones in the literature.
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7018898
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3982432
OpenAlex ID: W2902825974
cites work: Numerical investigation of the Liebau phenomenon
cites work: An experimental investigation and a simple model of a valveless pump
cites work: On the pumping effect in a pipe/tank flow configuration with friction
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cites work: Pumping effects in models of periodically forced flow configurations
cites work: Nicholson's blowflies differential equations revisited: main results and open problems
cites work: Existence of positive periodic solutions of first-order neutral differential equations
cites work: Nonoscillatory solutions of higher order differential and delay differential equations with forcing term
cites work: Existence of periodic solution for nonlinear differential equations.
Wikidata QID: Q128855449
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description: scientific article; zbMATH DE number 7018898