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Information × Registration Number 0211U000858, 0106U002559 , R & D reports Title The construction of the homogenized models of physical processes in micro-inhomogeneous media. popup.stage_title 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 popup.description2 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 popup.authors 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 popup.nrat_date 2020-04-02 Close