Title | Dimensionality reduction in inverse diffusion problem by means of numerical optimization methods |
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Authors | A. O. Syromyasov^{1}, D. V. Galkin^{1}, A. S. Shurshina^{2}, M. V. Shamolin^{3}^{1}National Research Ogarev Mordovia State University ^{2}Bashkir State University ^{3}Lomonosov Moscow State University |

Annotation | Article discusses the problem of determination of variable diffusion coefficient when the average concentration of admixture in organic film is measured and known in some moments of time. The problem is hard to solve for two reasons. First, the diffusion coefficient depends on large amount of parameters. Second, the dependence of average concentration on these parameters is complicated. The hypothesis is proposed that allows to find some of the parameters independently from others. Results of corresponding numerical experiment are stated. |

Keywords | inverse diffusion problem, least squares method, numerical optimization. |

Citation | Syromyasov A. O., Galkin D. V., Shurshina A. S., Shamolin M. V. ''Dimensionality reduction in inverse diffusion problem by means of numerical optimization methods'' [Electronic resource]. Proceedings of the XIV International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 9-12, 2019). Saransk: SVMO Publ, 2019. - pp. 156-159. Available at: http://conf.svmo.ru/files/2019/papers/paper41.pdf. - Date of access: 18.10.2021. |

**© SVMO, National Research Mordovia State University, 2021**

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