Registration Number
0221U101478,
0118U003138
, R & D reports
Title
Properties of singular solutions of differential equations, spectral analysis of difference systems and nonlinear processes simulation
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Head
Rassokhina Yuliia V.,
Registration Date
21-01-2021
Organization
Vasyl' Stus Donetsk National University
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Precise conditions of removability of isolated singularity for anisotropic p-Laplace equation with an absorption term, the regularity of solutions of quasilinear equations with nonstandard growth conditions, local properties (continuity and precise pointwise estimates of the Harnack type) for double phase parabolic equations are obtained in the project. The solvability of the Dirichlet and Neumann problems for a model nonlinear degenerate anisotropic elliptic equation of second order is investigated, and the conditions for the convergence of solutions are obtained. A systematic classification of generalized boundary triplets of symmetric linear operators in Hilbert space is given, different classes of generalized boundary triplets are characterized by purely analyticity through the Weyl function, the close interrelationships between different classes of boundary triples and the corresponding Weyl functions are investigated, the solution of the problem of realization of analytical R-functions in the form of Weyl functions of generalized boundary triples is obtained. Generalized boundary triplets for the Laplace operator in domains with nonsmooth boundaries are constructed, a method for describing polynomials satisfying S. Haruki's generalized conditions is developed, the dynamics of nonlinear processes described by differential equations with momentum and noise is investigated, and modeling of multiphase diffuse processes is performed.
Product Description
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Buryachenko Kateryna O.
Gorban Yuliya S
Derkach Volodymyr O.
Kovalyov Ivan M.
Krizhanovski Volodymyr G.
Skrypnik Igor I.
Trofymenko Olha D.
Shan Mariia O.
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2021-01-21
