Skip to main content
SpringerLink
Log in

Integral equations related to the study of an inverse coefficient problem for a system of partial differential equations

  • Integral Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We consider an inverse coefficient problem for a linear system of partial differential equations. The values of one solution component on a given curve are used as additional information for determining the unknown coefficient. The proof of the uniqueness of the solution of the inverse problem is based on the analysis of the unique solvability of a homogeneous integral equation of the first kind. The existence of a solution of the inverse problem is proved by reduction to a system of nonlinear integral equations.

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. Tikhonov, A.N. and Samarskii, A.A., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Izd. Moskov. Gos. Univ., 1999.

    Google Scholar 

  2. Lavrent’ev, M.M., Romanov, V.G., and Shishatskii, S.P., Nekorrektnye zadachi matematicheskoi fiziki i analiza (Ill-Posed Problems of Mathematical Physics and Analysis), Moscow: Nauka, 1980.

    Google Scholar 

  3. Romanov, V.G., Obratnye zadachi matematicheskoi fiziki (Inverse Problems of Mathematical Physics), Moscow: Nauka, 1984.

    MATH  Google Scholar 

  4. Denisov, A.M., Vvedenie v teoriyu obratnykh zadach (Introduction to Theory of Inverse Problems), Moscow, 1994.

    Google Scholar 

  5. Prilepko, A.I., Orlovsky, D.G., and Vasin, I.V., Methods for Solving Inverse Problems in Mathematical Physics, New York, 2000.

    MATH  Google Scholar 

  6. Kabanikhin, S.I., Obratnye i nekorrektnye zadachi (Inverse and Ill-Posed Problems), Novosibirsk, 2008.

    Google Scholar 

  7. Park, H.M. and Chung, O.Y., Inverse Natural Convection Problem of Estimating Wall Heat Flux Using a Moving Sensor, J. Heat Transfer, 1999, vol. 121, no. 4, pp. 828–836.

    Article  Google Scholar 

  8. Denisov, A.M., Integro-Differential Equations for the Problem of Determining the Source in the Wave Equation, Differ. Uravn., 2006, vol. 42, no. 9, pp. 1155–1165.

    MathSciNet  Google Scholar 

  9. Park, H.M. and Choi, Y.I., Estimation of Inhomogeneous Zeta Potential in the Electroosmotic Flow Using a Moving Sensor, Colloids and Surfaces A, 2007, vol. 307, pp. 93–99.

    Article  Google Scholar 

  10. Denisov, A.M., Inverse Problems for a Quasilinear Hyperbolic Equation in the Case of a Moving Observation Point, Differ. Uravn., 2009, vol. 45, no. 11, pp. 1543–1553.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    A. M. Denisov

Authors
  1. A. M. Denisov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. M. Denisov.

Additional information

Original Russian Text © A.M. Denisov, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 9, pp. 1187–1194.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Denisov, A.M. Integral equations related to the study of an inverse coefficient problem for a system of partial differential equations. Diff Equat 52, 1142–1149 (2016). https://doi.org/10.1134/S0012266116090056

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266116090056

Search

Navigation