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Journal of Mathematical Sciences

, Volume 170, Issue 2, pp 173–191 | Cite as

Problem of small and normal oscillations of a rotating elastic body filled with an ideal barotropic liquid

  • D. A. Zakora
Article
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Abstract

An evolutionary problem of small motions of an ideal barotropic liquid filling a rotating isotropic elastic body is studied in the paper. Moreover, the corresponding spectral problem arising in the study of normal motions of the mentioned system is considered. First, we state the evolutionary problem, then we pass to a second-ordered differential equation in some Hilbert space. Based on this equation, we prove the uniqueness theorem for the strong solvability of the corresponding mixed problem. The spectral problem is studied in the second part of the paper. A quadratic spectral sheaf corresponding to the spectral problem was derived and studied. Problems of localization, discreteness, and asymptotic form of the spectrum are considered for this sheaf. The statement of double completeness with a defect for a system of eigenelements and adjoint elements and the statement of essential spectrum of the problem are proved.

Keywords

Hilbert Space Cauchy Problem Strong Solution Elastic Body Spectral Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Faculty of Mathematics and Informatics, Chair of Mathematical AnalysisTaurida National V. I. Vernadsky UniversitySimferopolUkraine

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