Geodesic
On the application of the Galerkin projection method to the nonstationary diffusion equation with a variable coefficient
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4, Tome 233 (2024), pp. 89-98

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In this paper, we present an algorithm for applying the Galerkin projection method to solve a two-dimensional nonstationary diffusion equation with a variable coefficient. The concentration of nonequilibrium minority charge carriers was found in the form of a partial sum of a double Fourier series using a system of modified Laguerre functions. The results of calculations are presented for parameters characteristic of exciton diffusion in single-crystal gallium nitride.
Mots-clés : diffusion equation, Laguerre functions
Keywords: Galerkin projection method, concentration of minority charge carriers, order error estimate, modulus of continuity 
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     title = {On the application of the {Galerkin} projection method to the nonstationary diffusion equation with a variable coefficient},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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E. V. Seregina; M. A. Stepovich; M. N. Filippov. On the application of the Galerkin projection method to the nonstationary diffusion equation with a variable coefficient. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4, Tome 233 (2024), pp. 89-98. http://geodesic.mathdoc.fr/item/INTO_2024_233_a7/