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Information × Registration Number 0221U102576, 0116U005036 , R & D reports Title Geometric and asymptotic methods in the theory of boundary value problems of mathematical physics popup.stage_title Head Khruslov Evgen Ya., Доктор фізико-математичних наук Registration Date 05-02-2021 Organization B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine popup.description2  2. The following results were obtained. Homogenized models of stationary and nonstationary diffusion in strongly porous media with nonlinear absorption on the boundary, as well as suspension motion for two qualitatively different flow regimes: filtration regime and frozen particle regime are constructed. The asymptotic behavior of the Maxwell operator in media with ideally conducting inclusions of the trap type is investigated and a mathematical model of the photon metamaterial is constructed. The questions of existence and stability of solutions of a nonlinear problem with a free boundary are studied. The asymptotic behavior of the first eigenvalues and eigenfunctions of singularly perturbed elliptic operators is investigated. Analogues of Hilbert's classical theorem on the impossibility of global or local immersions of a two-dimensional Lobachevsky plane into a four-dimensional Euclidean space in the form of a pseudospherical surface with flat normal connection are proved. A generalization of Dini pseudospherical surfaces in the form of two-dimensional helicoidal surfaces in four-dimensional Euclidean space formed by helical rotation of spatial circular tractrices is proposed. Theorems that partially confirm Hopf's hypothesis of the existence of positive curvature metrics on the product of two-dimensional spheres are proved. The foliated analogue of Milnor's hypothesis about the fundamental group of layers of the nonnegative Ricci curvature on multidimensional compact manifolds is confirmed. The exact inverse isoperimetric inequality for regions of the Alexandrov plane of bounded curvature from below is proved. Theorems on the cylindricality of Finsler submanifolds of the nonnegative Ricci curvature in Minkowski space are proved. A classification of closed geodesics without self-intersection points on regular tetrahedra of Lobachevsky space is obtained and asymptotic estimates of the number of such geodesics are found. Product Description popup.authors popup.nrat_date 2021-02-05 Close