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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
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##### 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
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