Registration Number
0211U000858,
0106U002559
, R & D reports
Title
The construction of the homogenized models of physical processes in micro-inhomogeneous media.
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Head
Khruslov Ievgen Yakovych,
Registration Date
25-02-2011
Organization
B.Verkin Institute for Low Temperature Physics and Engineering of National Academy of Science of Ukraine
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Keywords: homogenized equations; quasi-linear elliptic equations; Sobolev spaces of non-standard growth; perforated domains; double porosity model; two-scale convergence; Г - convergence; the system of Navier-Stokes-Fokker-Planck equations; dynamics of the suspensions; the Ginzburg-Landau functional; vortices; the variational problems with loss of compactness; microheterogeneous media; particle clouds; particles settling. Objects of research: variational problems in perforated domains; variational problems in the media with double porosity; parabolic equations with nonstandard growth and with asymptotically degenerate coefficients; variational problems for the Ginzburg-Landau with prescribed degrees of mapping on the boundary, the problem of flow of suspensions, which are described by the Navier-Stokes -Fokker-Planck equations. Purposes: homogenization of linear and nonlinear elliptic and parabolic equations describing the flow of non-Newtonian and Newtonian fluids in porous media; homogenization of the Cauchy problem for evolution equations; construction of the homogenized (macroscopic) models of structured fluids; study of the asymptotic behavior of solutions of equations, modeling the dynamics of structured fluids; modeling of settling and drift of the cloud of solid particles, investigation of the existence of solutions of initial boundary value problem for the system of Navier-Stokes-Fokker-Planck equation. Research methods: E.Y. Khruslov's method of local energy characteristics; method of Г-convergence; two-scale convergence method, variational methods of the homogenization theory; methods of functional analysis and complex variable theory; methods of spectral theory for operators and operator pencils; numerical methods for the Navier-Stokes equation.
Product Description
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Бережний Максим Анатолійович
Гончаренко Марія Віталіївна
Зуєва Тетяна Іванівна
Панкратов Леонід Сергійович
Радякін Микола Костянтинович
Рибалко Володимир Олександрович
Фенченко Володимир Миколайович
Храбустовський Андрій Володимирович
Хруслов Євген Якович
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2020-04-02
