Geodesic
On the search for moment functions of a solution of the stochastic diffusion equation by the projection method
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 105-114

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In this paper, we present some results of the application of the projection method of least squares for the search for the first- and second-order moment functions of the solution of the two-dimensional equation of exciton diffusion with a random coefficient. An estimate of the error for the quadratic functional is obtained. Results of computational experiments for the parameters characteristic of gallium nitride are presented.
Mots-clés : diffusion equation, Laguerre functions
Keywords: projection method of least squares, expectation, autocorrelation function, modulus of continuity. 
@article{INTO_2021_200_a11,
     author = {E. V. Seregina and M. A. Stepovich and A. M. Makarenkov},
     title = {On the search for moment functions of a solution of the stochastic diffusion equation by the projection method},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {105--114},
     publisher = {mathdoc},
     volume = {200},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_200_a11/}
}
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E. V. Seregina; M. A. Stepovich; A. M. Makarenkov. On the search for moment functions of a solution of the stochastic diffusion equation by the projection method. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 105-114. http://geodesic.mathdoc.fr/item/INTO_2021_200_a11/