Geodesic
Problem on small motions and normal oscillations of capillary viscous liquids in rotating vessels
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 29 (2008), pp. 71-102

Voir la notice de l'article provenant de la source Math-Net.Ru

The new recent results of the author are applied to study the problem. We begin from the problem posing. Then we consider the problem as a system of operator equations in a Hilbert space. Further, the initial-boundary value problem is reduced to the Cauchy problem for the abstract parabolic equation; this allows us to prove the unique solvability theorem. Then we study normal oscillations of the hydraulic system under the assumption of static stability with respect to the linear approximation. We prove results about the spectrum of the problem and prove that the system of root functions (eigenfunctions and associated functions) form a basis. Also, we prove that if the static stability assumption is not satisfied, then the inversion of Lagrange's theorem on the stability is valid. 
@article{CMFD_2008_29_a5,
     author = {N. D. Kopachevskii},
     title = {Problem on small motions and normal oscillations of capillary viscous liquids in rotating vessels},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {71--102},
     publisher = {mathdoc},
     volume = {29},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2008_29_a5/}
}
TY  - JOUR
AU  - N. D. Kopachevskii
TI  - Problem on small motions and normal oscillations of capillary viscous liquids in rotating vessels
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2008
SP  - 71
EP  - 102
VL  - 29
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2008_29_a5/
LA  - ru
ID  - CMFD_2008_29_a5
ER  - 
%0 Journal Article
%A N. D. Kopachevskii
%T Problem on small motions and normal oscillations of capillary viscous liquids in rotating vessels
%J Contemporary Mathematics. Fundamental Directions
%D 2008
%P 71-102
%V 29
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2008_29_a5/
%G ru
%F CMFD_2008_29_a5
N. D. Kopachevskii. Problem on small motions and normal oscillations of capillary viscous liquids in rotating vessels. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 29 (2008), pp. 71-102. http://geodesic.mathdoc.fr/item/CMFD_2008_29_a5/