Abstract
We consider the problem of a nonsteady flow of a nonlinear viscous fluid in an oscillating tube. In this problem, the oscillations of the tube define the shape of the domain in which the fluid flows, this domain is changing in time, and the flow of the fluid influences the oscillations of the tube. So one has to solve a coupled system of equations of forced oscillations of the tube and of a flow of a fluid in a varying domain, and this domain is to be found. Such a problem is formulated and studied, and for small data, the existence of a solution is proven.
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Litvinov, W.G. (1998). An evolutionary problem of a flow of a nonlinear viscous fluid in a deformable viscoelastic tube. In: Gohberg, I., Mennicken, R., Tretter, C. (eds) Differential and Integral Operators. Operator Theory: Advances and Applications, vol 102. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8789-2_10
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DOI: https://doi.org/10.1007/978-3-0348-8789-2_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9774-7
Online ISBN: 978-3-0348-8789-2
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