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Information × Registration Number 0121U108115, ( 0226U001834  ) R & D request Title Analytical and asymptotic methods of mathematical physics and geometry Head Khruslov Yevhen Ya., д.ф.-м.н. Registration Date 10-02-2021 Organization B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine popup.description1 The main goal of the study is to develop analytical, asymptotic, topological and numerical methods for solving the problems of mathematical physics and geometry, the importance of which is due to their possible application in mathematical modeling of physical and biological processes of complex structure. It is assumed to study boundary value problems for nonlinear differential equations with a free boundary that arise in models of cell motility and growth of living tissues. A theoretical description of the autolocalized state of an electron due to its interaction with helium vapor atoms or liquid helium in the three-dimensional case will be given. It is assumed to investigate the asymptotic behavior of differential operators on Riemannian and pseudo-Riemannian manifolds of complex microstructure of increasing order and it is assumed to construct homogenized equations that describe the asymptotics. Homogenized models of electrodynamics of reticulated structures will be built. Within the framework of multidimensional differential geometry the properties of curvature and torsion of subtypes of Euclidean and Riemannian spaces and also the properties of layers on closed Riemannian manifolds with limited mean curvature of layers will be studied. It is planned to develop the theory of generalized Bianca-Backlund transformations for multidimensional pseudospherical submanifolds and for solutions of the corresponding integrated systems of differential equations. Using combinatorial, geometric and variational methods, it is planned to investigate the deformation properties of polyhedra associated with mathematical modeling of the instability of polyhedral structures. popup.nrat_date 2024-12-09 Close