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Information × Registration Number 0220U100481, 0116U003127 , R & D reports Title Fractional calculus, non-Archimedean and spectral analysis in the problems of the theory of differential equations and mathematical physics popup.stage_title Head Kochubei Anatolii N., Registration Date 20-10-2020 Organization The Institute of Mathematics of NASU popup.description2  The objects of study are linear and nonlinear differential and pseudodifferential equations that appear in models of mathematical physics. The purpose of the work is to develop methods of linear and nonlinear functional analysis, non-Archimedean and fractional calculus, and their applications to models of modern mathematical physics. Methods - spectral, variational, theory of potential, a priori estimates, analysis on infinite-dimensional groups, analysis on non-Archimedean fields, spaces of boundary values, calculations of quasi-derivatives, theorems on implicit function The results of works on the problems of linear and nonlinear functional analysis, non-Archimedean analysis, theory of differential and fractional-differential equations, spectral theory, closely related to the problems of mathematical physics, are presented. In particular, nonlinear pseudodifferential equations over the field of p-adic numbers, a fractional-type equation that describes the slow increase in quantities in physical and environmental models, are investigated. A harmonic analysis was developed on infinite-dimensional groups. New results are obtained in the theory of elliptic and parabolic boundary value problems in generalized Sobolev spaces, as well as in the spectral theory of strongly singular differential operators. Product Description popup.authors Antoniouk Alexandra V. Kosiak Olexander V. Mikhailets Volodymyr A. Murach Oleksandr O. popup.nrat_date 2020-04-01 Close