Computational Mathematics and Modeling

, Volume 30, Issue 4, pp 403–412 | Cite as

The Inverse Problem for an Integro-Differential Equation and its Solution Method

  • A. M. DenisovEmail author
  • A. A. Efimov

The inverse problem of the determination of the unknown coefficient in an integro-differential equation is considered. Existence and uniqueness theorems are proved for the inverse problem. A numerical method for the determination of the unknown coefficient is proposed and substantiated. Numerical results illustrating the convergence of the method are reported.


inverse problem integro-differential equation existence theorem for the inverse problem uniqueness theorem for the inverse problem 


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  1. 1.
    A. Lorenzi, “An identification problem related to a nonlinear hyperbolic integro-differential equation,” Nonlinear Analysis: Theory, Methods and Applications, 22(1), 297–321 (1994).MathSciNetCrossRefGoogle Scholar
  2. 2.
    J. Janno and L. Von Wolfersdorf, “An inverse problem for identification of a time and space-dependent memory kernel in viscoelastisity,” Inverse Problems, 17, 13–24 (2001).MathSciNetCrossRefGoogle Scholar
  3. 3.
    F. Colombo and D. Guidetti, “A global in time existence and uniqueness results for a semilinear integro-differential parabolic inverse problem in Sobolev spaces,” Math. Methods in Appl. Sciences, 17, 1–29 (2007).CrossRefGoogle Scholar
  4. 4.
    D. N. Durdiev, “Global solvability of the inverse problem for an integro-differential equation of electrodynamics,” Diff. Uravn., 44(7), 893–899 (2008).MathSciNetCrossRefGoogle Scholar
  5. 5.
    S. A. Avdonin, S. A. Ivanov, and J. M. Wang, “Inverse problems for the heat equation with memory,” American Institute of Mathematical Sciences,13(1), 31–38 (2019).Google Scholar
  6. 6.
    A. M. Denisov and S. R. Tuikina, “On some inverse problem of nonequilibrium sorption dynamics,” Dokl. AN SSSR, 276(1), 100–102 (1984).Google Scholar
  7. 7.
    A. Lorenzi and E. Papazoni, “An inverse problem arising in the theory of absorption,” Appl. Anal., 36(2), 249–263 (1990).MathSciNetCrossRefGoogle Scholar
  8. 8.
    A. M. Denisov, and A. Lorenzi, “Recovering an unknown coefficient in an absorption model with diffusion,” J. Inverse and Ill-Posed Problems, 15(6), 599–610 (2007).Google Scholar
  9. 9.
    A. M. Denisov, “Inverse problem for a quasi-linear system of partial differential equations with a nonlocal boundary condition,” Zh. Vychisl. Matem. i Mat. Fiz., 54(10), 1571–1579 (2014).Google Scholar
  10. 10.
    S. R. Tuikina and S. I. Solov’eva, “Numerical solution of an inverse problem for a two-dimensional mathematical model of sorption dynamics.” Computational Mathematics and Modeling, 23(1), 34–41.MathSciNetCrossRefGoogle Scholar
  11. 11.
    S. R. Tuikina, “Numerical determination of two sorbent characteristics from dynamic observations,” Computational Mathematics and Modeling, 29(3), 299–306 (2018).MathSciNetCrossRefGoogle Scholar
  12. 12.
    A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Izd. MGU, Moscow (1999).Google Scholar
  13. 13.
    A. M. Denisov and A. V. Lukshin, Mathematical Models for One-Component Sorption Dynamics [in Russian], Izd. MGU, Moscow (1989).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia

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