- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2021 14 (5)
- Authors
- Denisenko, Valery V.; Nesterov, Semen A.
- Contact information
- Denisenko, Valery V.: Institute of Computational Modelling SB RAS Krasnoyarsk, Russian Federation; OCRID: 0000-0002-3024-3746; Nesterov, Semen A.: Institute of Computational Modelling SB RAS Krasnoyarsk, Russian Federation; OCRID: 0000-0002-9409-5826
- Keywords
- mathematical modeling; energy method; elliptic equation; asymmetric operator
- Abstract
Three-dimensional elliptic boundary value problems arising in the mathematical modeling of quasi-stationary electric fields and currents in conductors with gyrotropic conductivity tensor in domains homeomorphic to the spherical layer are considered. The same problems are mathematical models of thermal conductivity or diffusion in moving or gyrotropic media. The operators of the problems in the traditional formulation are non-symmetric. New statements of the problems with symmetric positive definite operators are proposed. For the four boundary value problems the quadratic energy functionals, to the minimization of which the solutions of these problems are reduced, are constructed. Estimates of the obtained quadratic forms are made in comparison with the form appearing in the Dirichlet principle for the Poisson equation
- Pages
- 554–565
- DOI
- 10.17516/1997-1397-2021-14-5-554-565
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/143728
Journal of Siberian Federal University. Mathematics & Physics / Energy Method for the Elliptic Boundary Value Problems with Asymmetric Operators in a Spherical Layer
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