| 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:
|
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 1987-8. |
| Reference:
|
[2] V. Lovicar: .Private communication. Zbl 0793.34040 |
| . |
