Mathematical analysis of the small oscillation of a heavy heterogeneous viscous liquid in an open immovable container
Abstract
The aim of this paper is the study of the influence of the viscosity on the oscillations of a heterogeneous liquid in a container. Above all, it is proved that the presence of viscosity removes the essential spectrum which appears in the case of a heterogeneous inviscid liquid. From the equations of the system container-liquid, we deduce the variational equation of the problem, and then an operatorial equation in a suitable Hilbert space. The study of the normal oscillations is reduced to the study of an operator bundle whose kind is well known. We obtain an infinity of a periodic damped motions and, for sufficiently small viscosity, a finite number of oscillatory damped motions. The existence and uniqueness of the associated evolution problem are then proved using the weak formulation.
- Published
- 12 October 2013
- Volume
- 2014 (2014)
- License
- CC BY 3.0
Copyright © 2013 H. Essaouini, J. Elbahaoui, L. Elbakkali, P. Capodanno. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
H. Essaouini, J. Elbahaoui, L. Elbakkali, P. Capodanno, Mathematical analysis of the small oscillation of a heavy heterogeneous viscous liquid in an open immovable container, Eng. Math. Lett. 2014 (2014), 2.
BibTeX
@article{Essaouini2014,
author = {Essaouini, H. and Elbahaoui, J. and Elbakkali, L. and Capodanno, P.},
title = {Mathematical analysis of the small oscillation of a heavy heterogeneous viscous liquid in an open immovable container},
journal = {Eng. Math. Lett.},
volume = {2014},
year = {2014},
pages = {2},
doi = {}
}