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

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 -