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Asymptotic Solution of Coefficient Inverse Problems for Burgers-Type Equations

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Abstract

For a singularly perturbed reaction–diffusion–advection equation, called in applications a Burgers-type equation and having a time-periodic solution with an internal transition layer, asymptotic analysis is used to solve some inverse problems of reconstructing model parameters (determining the linear amplification factor and boundary conditions) from known information about the observed solution of the direct problem in a given time interval (period). Numerical experiments demonstrating the efficiency of the approach proposed are conducted.

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ACKNOWLEDGMENTS

We are grateful to A.G. Yagola and D.V. Luk’yanenko for discussing this work, which contributed to its improvement. In addition, we thank D.V. Luk’yanenko for conducting experiments illustrating the efficiency of the approach developed.

Funding

This work was supported by the Russian Science Foundation, grant no. 18-11-00042.

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Authors and Affiliations

  1. Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia

    V. T. Volkov & N. N. Nefedov

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  1. V. T. Volkov
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  2. N. N. Nefedov
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Correspondence to N. N. Nefedov.

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Translated by E. Chernokozhin

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Volkov, V.T., Nefedov, N.N. Asymptotic Solution of Coefficient Inverse Problems for Burgers-Type Equations. Comput. Math. and Math. Phys. 60, 950–959 (2020). https://doi.org/10.1134/S0965542520060123

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  • DOI: https://doi.org/10.1134/S0965542520060123

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