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Information × Registration Number 0222U000064, 0121U110543 , R & D reports Title Algebraic and analytical methods in the theory of partial differential equations popup.stage_title Head Vanieieva Olena O., Доктор фізико-математичних наук Registration Date 02-01-2022 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 The aim of this work is to develop new and improve existing algebraic and analytical methods for studying differential equations with partial derivatives. Concerning algebraic methods, the main attention is paid to the classification of Lie symmetries in classes of differential equations that model physical, biological, and economic processes. These include the important for applications (2+1)-dimensional Burgers equation, the variable coefficient Klein-Gordon equations, and others. In particular, the aim of the work is to obtain exhaustive Lie symmetry classifications for the equations under study and to construct their exact solutions. As to analytical tools of the study of multidimensional differential equations, the project participants will aim at the developing of the method of scales of function spaces and at the method of the interpolation of pairs of normed spaces and operators on them. We plan to introduce broad classes of the generalized Sobolev, Nikolskii–Besov, and Triebel–Lizorkin spaces that have interpolation properties with respect to their classical analogs and allow a correct definition on smooth manifolds. We expect to build a new theory of solvability of elliptic differential equations and elliptic boundary-value problems on manifolds in classes of the spaces introduced. A specific attention will be paid to elliptic problems with rough (i.e. irregular) data, specifically to problems with white noise in boundary conditions, which arise in physics and technology. Thus, a number of new algorithms were proposed to study the symmetric properties of complex nonlinear differential equations and effective methods for constructing their exact solutions. Product Description popup.authors Anop Annа V. Lokaziuk Oleksandra V Satur Oksana R Chepurukhina Iryna S. popup.nrat_date 2022-03-09 Close