Dynamics of small bubble interface perturbations in vertical hele-shaw cell with magnetic liquid under the action of normal magnetic field

A linearized problem of dynamics for small perturbations of the gas bubble rising in the Hele-Shaw cell filled with magnetic liquid is considered. It is reduced to searching of eigenvalues and eigenfunctions for a linear operator with periodic boundary conditions. The obtained operator is presented...

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Vydané v:	Mathematical modelling and analysis Ročník 9; číslo 4; s. 287 - 298
Hlavní autori:	Cirulis, T., Lietuvietis, O., Cēbers, A.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Taylor & Francis Group 01.01.2004
Predmet:	Chebyshev polynomials eigenvalues and eigenfunctions problem gas bubble Hele-Shaw cell magnetic liquid the Degenerate Matrices method
ISSN:	1392-6292, 1648-3510
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Popis
Shrnutí:	A linearized problem of dynamics for small perturbations of the gas bubble rising in the Hele-Shaw cell filled with magnetic liquid is considered. It is reduced to searching of eigenvalues and eigenfunctions for a linear operator with periodic boundary conditions. The obtained operator is presented as a sum of two linear operators: the second order differential operator with varying coefficients and the integro - differential operator with the singularity of the Cauchy type. The spectral problem is solved by the Degenerate Matrices (DM) method using Chebyshev polynomials of the first and second kind.
ISSN:	1392-6292 1648-3510
DOI:	10.1080/13926292.2004.9637260