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Application of Asymptotic Analysis for Solving the Inverse Problem of Determining the Coefficient of Linear Amplification in Burgers’ Equation

  • Theoretical and Mathematical Physics
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Moscow University Physics Bulletin Aims and scope

Abstract

Asymptotic analysis of a singularly perturbed reaction—diffusion—advection equation, which is called a Burgers-type equation in applications and has a solution with a sharp transition layer, is applied to solve the coefficient inverse problem of determining the coefficient of linear amplification from known information on the observed solution of the direct problem at the final moment of time. The efficiency of the approach proposed in this study is shown using a series of model numerical experiments.

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References

  1. N. N. Nefedov and O. V. Rudenko, Dokl. Math. 97, 99 (2018).

    Article  MathSciNet  Google Scholar 

  2. D. V. Lukyanenko, V. T. Volkov, and N. N. Nefedov, Model. Anal. Inf. Sist. 24, 322 (2017).

    Article  MathSciNet  Google Scholar 

  3. D. Lukyanenko, N. Nefedov, E. Nikulin, and V. T. Volkov, Lect. Notes Comput. Sci. 10187, 107 (2017).

    Article  Google Scholar 

  4. A. Melnikova, N. Levashova, and D. Lukyanenko, Lect.Notes Comput.Sci. 10187, 492 (2017).

    Article  Google Scholar 

  5. E. A. Antipov, V. T. Volkov, N. T. Levashova, and N. N. Nefedov, Model. Anal. Inf. Sist. 24, 259 (2017).

    Article  MathSciNet  Google Scholar 

  6. E. A. Antipov, N. T. Levashova, and N. N. Nefedov, Comput. Math. Math. Phys. 54, 1536 (2014).

    Article  MathSciNet  Google Scholar 

  7. D. V. Lukyanenko, M. A. Shishlenin, and V. T. Volkov, Commun. Nonlinear Sci. Numer. Simul. 54, 233 (2018).

    Article  MathSciNet  ADS  Google Scholar 

  8. D. V. Lukyanenko, V. B. Grigorev, V. T. Volkov, and M. A. Shishlenin, Comput. Math. Appl. 77, 1245 (2019).

    Article  MathSciNet  Google Scholar 

  9. V. T. Volkov, N. E. Grachev, N. N. Nefedov, and N. A. Nikolaev, Comput. Math. Math. Phys. 47, 1301 (2007).

    Article  MathSciNet  Google Scholar 

  10. A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Kluwer Academic, 1995).

  11. M. M. Lavrentiev, Rep. USSR Acad. Sci. 127, 31 (1959).

    Google Scholar 

  12. A. N. Tikhonov, Rep. USSR Acad. Sci. 153, 49 (1963).

    Google Scholar 

  13. V. V. Vasin and A. L. Ageev, Ill-Posed Problems with a Priori Information (VSP, Utrecht, 1995).

    Book  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Physics, Moscow State University, Moscow, 119991, Russia

    D. V. Lukyanenko, V. T. Volkov, N. N. Nefedov & A. G. Yagola

Authors
  1. D. V. Lukyanenko
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  2. V. T. Volkov
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  3. N. N. Nefedov
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  4. A. G. Yagola
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Corresponding authors

Correspondence to D. V. Lukyanenko or V. T. Volkov.

Additional information

Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Seriya 3: Fizika, Astronomiya, 2019, No. 2, pp. 38–43.

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Lukyanenko, D.V., Volkov, V.T., Nefedov, N.N. et al. Application of Asymptotic Analysis for Solving the Inverse Problem of Determining the Coefficient of Linear Amplification in Burgers’ Equation. Moscow Univ. Phys. 74, 131–136 (2019). https://doi.org/10.3103/S0027134919020127

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  • DOI: https://doi.org/10.3103/S0027134919020127

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