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Information × Registration Number 0121U110543, ( 0222U000064  0223U000172  ) R & D request Title Algebraic and analytical methods in the theory of partial differential equations Head Vanieieva Olena O., Доктор фізико-математичних наук Registration Date 14-04-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description1 The aim of the project is to develop new algebraic and analytical methods of investigation of partial differential equations. As for algebraic methods the main attention will be paid for classification of Lie symmetries for classes of multidimensional nonlinear partial differential equations that model physical and biological processes. Enhanced and modified existing techniques of group analysis of differential equations will be used in the project. These techniques will be applied, in particular, to reaction–diffusion equations, Fisher equations, Burgers equations and Klein–Gordon equations with variable coefficients that are important for applications. We aim to get exhaustive Lie symmetry classifications and construct exact solutions for these equations. With regard to analytical tools, the study of multidimensional differential equations of the project participants will be aimed at developing a method of scales of functional spaces and a method of interpolation of pairs of normalized spaces and operators on them. It is planned to introduce broad classes of generalized spaces of Sobolev, Nikolsky–Besov, and Tribel–Lizorkin, which have interpolation properties with respect to their classical analogues and allow correct definition on smooth manifolds. A new theory of solvability of elliptic differential equations and elliptic boundary value problems on varieties in classes of introduced spaces is expected to be constructed. Particular attention will be paid to elliptic problems with coarse (ie irregular) data, in particular problems with white noise in boundary conditions, which arise in physics and technology. popup.nrat_date 2024-12-09 Close