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Features of Numerical Reconstruction of a Boundary Condition in an Inverse Problem for a Reaction–Diffusion–Advection Equation with Data on the Position of a Reaction Front

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Abstract

A new approach to the reconstruction of a boundary condition in an inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation with data on the reaction front position is proposed. The problem is solved via gradient minimization of a cost functional with an initial approximation chosen by applying asymptotic analysis methods. The efficiency of the proposed approach is demonstrated by numerical experiments.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 20-31-70016.

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Authors and Affiliations

  1. Faculty of Physics, Lomonosov Moscow State University, 119992, Moscow, Russia

    R. L. Argun, A. V. Gorbachev & D. V. Lukyanenko

  2. Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, 119234, Moscow, Russia

    D. V. Lukyanenko

  3. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    M. A. Shishlenin

  4. Novosibirsk State University, 630090, Novosibirsk, Russia

    M. A. Shishlenin

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  1. R. L. Argun
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  2. A. V. Gorbachev
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  3. D. V. Lukyanenko
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  4. M. A. Shishlenin
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Correspondence to D. V. Lukyanenko.

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Translated by I. Ruzanova

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Argun, R.L., Gorbachev, A.V., Lukyanenko, D.V. et al. Features of Numerical Reconstruction of a Boundary Condition in an Inverse Problem for a Reaction–Diffusion–Advection Equation with Data on the Position of a Reaction Front. Comput. Math. and Math. Phys. 62, 441–451 (2022). https://doi.org/10.1134/S0965542522030022

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