Open AccessTo the Problem on Small Motions of the System of Two Viscoelastic Fluids in a Fixed Vessel
Author(s) -
Nikolay D. Kopachevsky
Publication year - 2018
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2018-64-3-547-572
Subject(s) - operator (biology) , viscoelasticity , mathematics , pencil (optics) , initial value problem , hilbert space , mathematical analysis , compressibility , cauchy problem , physics , mechanics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene , thermodynamics
In this paper, we study the problem of small motions of two Oldroyd viscoelastic incompressible uids contained in a xed vessel. By means of the operator approach, we reduce the original initialboundary value problem to the Cauchy problem for a dierential operator equation in a Hilbert space and prove the well-posed solvability of the problem on an arbitrary interval of time. We obtain the equation for normal oscillations of the hydraulic system under consideration (Krein generalized operator pencil).