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Title: Solution of a linear model of a single-piston pump by means of methods for differential equations in Hilbert spaces (English)
Author: Straškraba, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 31
Issue: 6
Year: 1986
Pages: 461-479
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
Summary: A mathematical model of a fluid flow in a single-piston pump is formulated and solved. Variation of pressure and rate of flow in suction and delivery piping respectively is described by linearized Euler equations for barotropic fluid. A new phenomenon is introduced by a boundary condition with discontinuous coefficient describing function of a valve. The system of Euler equations is converted to a second order equation in the space $L^2(0,l)$ where $l$ is length of the pipe. The existence, unicity and stability of the solution of the Cauchy problem and the periodic solution is proved under explicit assumptions. (English)
Keyword: telegraph equation
Keyword: time-dependent boundary condition
Keyword: single-piston pump
Keyword: linearized Euler equations
Keyword: barotropic fluid
Keyword: boundary condition with discontinuous coefficient
Keyword: existence
Keyword: Cauchy problem
Keyword: periodic solution
Keyword: compressible fluid flow
MSC: 35B10
MSC: 35B35
MSC: 35L20
MSC: 76N10
idZBL: Zbl 0644.76081
idMR: MR0870482
DOI: 10.21136/AM.1986.104224
Date available: 2008-05-20T18:31:08Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] V. Kolarčík: Linear model of a piston pump.Communication during the cooperation of Mathematical Institute of Czechoslovak Academy of Sciences and Research Institute of Concern Sigma Olomouc in 1984. Also to appear in Acta Technica ČSAV 1987-8.
Reference: [2] V. Lovicar: .Private communication. Zbl 0793.34040


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