Skip to main content
SpringerLink
Log in

Nonlocal Inverse Problem for a Parabolic Equation with Degeneration

  • Published:
Ukrainian Mathematical Journal Aims and scope

We establish conditions for the existence and uniqueness of a classical solution of the inverse problem of determination of the time-dependent coefficient of the higher-order derivative in a parabolic equation with degeneration in the coefficient of the time derivative. We impose boundary conditions of the second kind and a nonlocal overdetermination condition. The case of weak degeneration is investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. F. Jones, “The determination of a coefficient in a parabolic differential equation. I. Existence and uniqueness,” J. Math. Mech., 11, No 5, 907–918.

  2. J. R. Cannon and W. Rundell, “Recovering a time-dependent coefficient in a parabolic differential equation,” J. Math. Anal. Appl., 160, 572–582 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Azari, C. Li, Y. Nie, and S. Shang, “Determination of an unknown coefficient in a parabolic inverse problem,” Dynamics of Continuous, Discrete, and Impulsive Systems. Ser. A: Math. Analysis, 11, 665–674 (2004).

    MATH  Google Scholar 

  4. I. B. Bereznyts’ka, A. I. Drebot, M. I. Ivanchov, and Yu. M. Makar, “Inverse problem for the heat-conduction equation with integral overdetermination,” Visn. Lviv. Univ., Ser. Mekh.-Mat., Issue 48, 71–79 (1997).

    Google Scholar 

  5. N. I. Ivanchov, “Inverse problems for the heat-conduction equation with nonlocal boundary conditions,” Ukr. Mat. Zh., 45, No. 8, 1066–1071 (1993); English translation: Ukr. Math. J., 45, No. 8, 1186–1192 (1993).

  6. Yin Hong-Ming, “Recent and new results on determination of unknown coefficients in parabolic partial differential equations with over-specified conditions,” in: Inverse Problems in Diffusion Processes (1995), pp. 181–198.

  7. M. Ivanchov, Inverse Problems for Equations of Parabolic Type, VNTL Publ., Lviv (2003).

    MATH  Google Scholar 

  8. N. V. Saldina, “Strongly degenerate inverse parabolic problem with general behavior of the coefficients,” Visn. Lviv. Univ., Ser. Mekh.-Mat., Issue 66, 186–202 (2006).

  9. N. Saldina, “An inverse problem for a generally degenerate heat equation,” Visn. Nats. Univ. “Lvivs’ka Politekhnika,” Fiz.-Mat. Nauk., Issue 566, 59–67 (2006).

  10. A. S. Kalashnikov, “On increasing solutions of linear equations of the second order with nonnegative characteristic form,” Mat. Zametki, 3, No 2, 171–178 (1968).

    MathSciNet  Google Scholar 

  11. M. Ivanchov and N. Hryntsiv, “Inverse problem for a weakly degenerate parabolic equation in a domain with free boundary,” J. Math. Sci., 167, No. 1, 16–29 (2010).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Franko Lviv National University, Lviv, Ukraine

    N. M. Huzyk

Authors
  1. N. M. Huzyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 6, pp. 765–779, June, 2013.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huzyk, N.M. Nonlocal Inverse Problem for a Parabolic Equation with Degeneration. Ukr Math J 65, 847–863 (2013). https://doi.org/10.1007/s11253-013-0822-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-013-0822-6

Keywords

Search

Navigation