Title:

Solution of a linear model of a singlepiston pump by means of methods for differential equations in Hilbert spaces (English) 
Author:

Straškraba, Ivan 
Language:

English 
Journal:

Aplikace matematiky 
ISSN:

03736725 
Volume:

31 
Issue:

6 
Year:

1986 
Pages:

461479 
Summary lang:

English 
Summary lang:

Russian 
Summary lang:

Czech 
. 
Category:

math 
. 
Summary:

A mathematical model of a fluid flow in a singlepiston 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:

timedependent boundary condition 
Keyword:

singlepiston 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:

20080520T18:31:08Z 
Last updated:

20200728 
Stable URL:

http://hdl.handle.net/10338.dmlcz/104224 
. 
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 19878. 
Reference:

[2] V. Lovicar: .Private communication. Zbl 0793.34040 
. 