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.
Burbulo paviršiaus mažų žadinimų dinamika vertikalioje Hele-Shaw ląstelėje, užpildytoje magnetiniu skysčių veikiamo normaliniu magnetiniu lauku
Santrauka. Dujų burbulo, judančio vertikalią Hele‐Shaw ląstelę užpildančiu magnetiniu skysčiu, paviršiaus dinamikos matematinis modelis yra suformuluotas kaip spektrinis uždavinys tam tikram tiesiniam operatoriui su periodinėmis kraštinėmis sąlygomis. Pastarasis uždavinys yra išspręstas skaitmeniškai išsigimstančių matricų metodu.
Cirulis, T., Lietuvietis, O., & Cēbers, A. (2004). Dynamics of small bubble interface perturbations in vertical hele‐shaw cell with magnetic liquid under the action of normal magnetic field. Mathematical Modelling and Analysis, 9(4), 287-298. https://doi.org/10.3846/13926292.2004.9637260
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