Registration Number
0226U002329,
(0121U100182)
, R & D reports
Title
Development of geometric, topological and approximate methods in the theory of nonclassical solutions of boundary value problems of mathematical physics
popup.stage_title
Розвиток геометричних, топологічних та апроксимативних методів в теорії некласичних розв’язків крайових задач математичної фізики
Head
Vladimir I. Ryazanov, д.ф.-м.н.
Registration Date
23-02-2026
Organization
Institute of Applied Mathematics and Mechanics National Academy of Science of Ukraine
popup.description1
The aim of this work is to develop a new direction in the theory of generalizations of quasiconformal mappings aimed at studying the fundamental boundary value problems in mathematical physics of Hilbert, Dirichlet, Neumann, Poincaré and Riemann with arbitrary boundary data measurable relative to the logarithmic measure for nonlinear degenerate PDE whose diffusion part takes into account the inhomogeneity and anisotropy of the medium and whose absorption part is nonlinear.
popup.description2
The object of research is boundary value problems of potential theory in anisotropic and inhomogeneous media, modern classes of functions and mappings. The purpose of the work is to develop a new direction in the theory of generalisations of quasi-conformal mappings, aimed at studying fundamental boundary value problems of mathematical physics of Hilbert, Dirichlet, Neumann, Poincaré, and Riemann with arbitrary boundary data measurable with respect to logarithmic measure for nonlinear PDEs with degeneracy of the uniform ellipticity condition, whose diffusion part takes into account the heterogeneity and anisotropy of the medium, and whose absorption part is nonlinear. Research methods include methods of modules, measure theory, complex analysis, approximation theory, general, algebraic and metric topology. Fundamentally new world-class theoretical results have been obtained, such as conditions for the existence, representation, and regularity of solutions to boundary value problems of Hilbert, Dirichlet, Neumann, Poincaré, and Riemann, both for non-continuous and arbitrary measurable boundary data for equations of the Beltrami, Vekua, Cauchy-Riemann and Poisson equations, and A-harmonic equations, as well as approximate, geometric, and topological methods that can be applied in mathematical modelling of diffusion with absorption, plasma and combustion states, liquid filtration in the development of oil fields and aquifers, cryptographic systems, justification of iterative methods, existence of fixed points in PDEs, topological analysis of large data sets, machine learning, analysis of dynamic systems and economic models.
Product Description
popup.authors
Viktoriia V. Bilet
Oleksiy A. Dovgoshiy
Tetiana V. Lomako
Volodymyr Y. Gutlyanskii
Olena S. Afanas'eva
Yuriy S. Kolomoitsev
Evgen A. Sevostyanov
Yevgen O. Petrov
Artem S. Yefimushkin
Olha V. Niesmielova
Ruslan V. Skuratovskyi
Artem R. Salimov
popup.nrat_date
2026-02-23
