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Цикл наукових праць "Аналітичні і алгебро-геометричні методи математичної фізики"


Authors:BogolubovМ.М.(jr.), Kovalevsky О.A.KochubeiA.N., MykytyukI.V., Prykarpatsky A.K., RebenkoО.L., SamoylenkoV.H.,TedeyevA.F.,ShishkovA.E.

Presentedby the Institute ofMathematics of NAS ofUkraine.

The series consists of 12monographsand 92scientific articlespublishedduring the period1975 –2012.

The series of papers is devoted to the study of current problems for dynamical systems of contemporary mathematical and theoretical physics as well as the constructing new effective methods for analysis of solutions to nonlinear partial differential equations and their applications to the study of mathematical models.

The papers deal with integrable systems, elliptic and parabolic partial differential equations and fractional differential equations describing the nonclassical diffusion (abnormally slow diffusion on fractals), homogenization and regimes with peaking, p-adic analysis and others.In so doing the mathematical objects of physical origin are studied by methods of various fields of mathematics, from functional analysis to algebraic geometry and the theory of Lie groups.

The authors develop such current trends of contemporary mathematical physics as analytical methods of the theory of boundary value problems for nonlinear elliptic and parabolic equations including those arising in the study of various physical phenomena, theory of evolution equations and general boundary problems, methods of non-Archimedean analysis and non-Archimedean stochastic and their applications, the theory of nonlinear dynamical systems of mathematical physics, analytical methods of infinite-dimensional analysis and their applications in quantum field theory and statistical mechanics.

Publications:17 monographs, 1108articles. Total number of references to publications of authors is 1037 (according to the SCOPUSdatabase), h-index= 19. 11 doctor's (DSc) and 27candidate's (PhD) theses have been defendedin the field.