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Existence of perturbed equilibrium states in some two-layer systems with density inversionстатья
Статья опубликована в журнале из списка RSCI Web of Science
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 11 января 2019 г.
- Автор: Georgievskii D.V.
- Журнал: Russian Journal of Mathematical Physics
- Том: 25
- Номер: 4
- Год издания: 2018
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 492
- Последняя страница: 499
- DOI: 10.1134/S1061920818040064
- Аннотация: In the system formed by a heavy elastic layer (lithosphere) and a half-space filled by an ideal incompressible fluid (asthenosphere), the possibility of the existence of equilibrium states with curved boundaries near an equilibrium of a system with rectilinear boundaries is investigated. Using an analysis of the characteristic equation, we obtain a relationship between the wave number of the desired static perturbation and the dimensionless parameters of the problem, namely, the dimensionless shear modulus, Poisson’s ratio, and the decompression. The assumption that the deformations are small imposes conditions on the ranges of modification of the quantities. For example, for a moderately compressible elastic material, the equilibrium which is called tectonic waves in geophysical applications is possible only in the long-wavelength range in the presence of the inversion of density and very strong decompression. The stability problem with respect to small dynamical perturbations of an (obtained) equilibrium with curved boundaries is stated. A wave dispersion relation connecting the complex frequency of oscillations with the wave number of perturbations and with the above dimensionless parameters of the system is derived.
- Добавил в систему: Георгиевский Дмитрий Владимирович