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Information × Registration Number 0223U000172, 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 04-01-2023 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 The aim of the work is to develop new algebraic and analytical methods for the study of partial differential equations and the application of such methods to classes of differential equations that are important for application. With regard to algebraic methods, the main attention of the project participants was paid to the problems of symmetry classification of classes of partial differential equations, in particular, classes of generalized equations of Kawahara, Fisher, d'Alembert, Laplace, as well as the description of admissible transformations for a class of normal linear systems. and equivalence groupoids of the class under consideration and its subclasses. Concerning analytical tools for studying multidimensional differential equations, the efforts of the project participants are aimed at constructing a new theory of solvability of elliptic boundary value problems in the classes of the introduced Sobolev, Nikolsky-Besov and Triebel-Lizorkin spaces of generalized smoothness. Elliptic boundary value problems with rough boundary data are studied in the classes of L_p-Sobolev spaces as being of low regularity. The goal is to establish local (up to the limit of the domain where the elliptic equation is specified) regularity and an a priori estimate of the generalized solution of such a problem. Pseudodifferential boundary value problems are studied in the scales of Nikol'skii-Besov and Triebel-Lizorkin spaces modified according to Roitberg. The goal is to prove that these problems are Fredholm (Noetherian) on pairs of the corresponding spaces. Also, the goal is to build models of dynamic conflict systems and study their properties. Product Description popup.authors Anop Annа V. Lokaziuk Oleksandra V Satur Oksana R Chepurukhina Iryna S. popup.nrat_date 2023-01-04 Close