×

zbMATH — the first resource for mathematics

Solution of a linear model of a single-piston pump by means of methods for differential equations in Hilbert spaces. (English) Zbl 0644.76081
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.

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B35 Stability in context of PDEs
35B10 Periodic solutions to PDEs
PDF BibTeX XML Cite
Full Text: EuDML
References:
[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.
[2] V. Lovicar: Private communication. · Zbl 0793.34040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.