# Solution of a linear model of a single-piston pump by means of methods for differential equations in Hilbert spaces

Aplikace matematiky (1986)

• Volume: 31, Issue: 6, page 461-479
• ISSN: 0862-7940

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## Abstract

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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 ${L}^{2}\left(0,l\right)$ 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.

## How to cite

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Straškraba, Ivan. "Solution of a linear model of a single-piston pump by means of methods for differential equations in Hilbert spaces." Aplikace matematiky 31.6 (1986): 461-479. <http://eudml.org/doc/15470>.

@article{Straškraba1986,
abstract = {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.},
author = {Straškraba, Ivan},
journal = {Aplikace matematiky},
keywords = {telegraph equation; time-dependent boundary condition; single-piston pump; linearized Euler equations; barotropic fluid; boundary condition with discontinuous coefficient; existence; Cauchy problem; periodic solution; compressible fluid flow; telegraph equation; time-dependent boundary condition; single-piston pump; linearized Euler equations; barotropic fluid; boundary condition with discontinuous coefficient; existence; Cauchy problem; periodic solution},
language = {eng},
number = {6},
pages = {461-479},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solution of a linear model of a single-piston pump by means of methods for differential equations in Hilbert spaces},
url = {http://eudml.org/doc/15470},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Straškraba, Ivan
TI - Solution of a linear model of a single-piston pump by means of methods for differential equations in Hilbert spaces
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 6
SP - 461
EP - 479
AB - 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.
LA - eng
KW - telegraph equation; time-dependent boundary condition; single-piston pump; linearized Euler equations; barotropic fluid; boundary condition with discontinuous coefficient; existence; Cauchy problem; periodic solution; compressible fluid flow; telegraph equation; time-dependent boundary condition; single-piston pump; linearized Euler equations; barotropic fluid; boundary condition with discontinuous coefficient; existence; Cauchy problem; periodic solution
UR - http://eudml.org/doc/15470
ER -

## References

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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. (1984)
2. V. Lovicar, [unknown], Private communication. Zbl0793.34040

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