Advertisement

Inverse Problems of Simultaneous Determination of the Time-Dependent Right-Hand Side Term and the Coefficient in a Parabolic Equation

  • Vitaly L. KamyninEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9045)

Abstract

This work deals with the inverse problem of simultaneous determination of two unknown time-dependent terms in a one-dimensional parabolic equation. The additional information is given by two integral observations. We prove theorems of existence and uniqueness of solution. We also give estimates of maximum modulus of unknown right-hand side and unknown coefficient of the equation with constants derived explicitly in terms of input data.

Notes

Acknowledgements

This work was supported by the Program for improving the competitiveness of universities (NRNU MEPHI).

References

  1. 1.
    Ivanchov, N.I.: On the inverse problem of simultaneous determination of the coefficients of heat conductivity and heat capacity. Siberian Math. J. 35(3), 612–621 (1994)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Anikonov, Y.E., Belov, Y.Y.: Determining two unknown coefficients of parabolic type equations. J. Inverse Ill-Posed Prob. 8(1), 1–19 (2000)CrossRefGoogle Scholar
  3. 3.
    Ivanchov, N.I., Pobyrivska, N.V.: On determination of two coefficients in parabolic equation depending on time. Siberian Math. J. 43(2), 402–413 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Kruzhkov, S.N.: Quasilinear parabolic equations and systems with two independent variables. Trudy Sem. im. I. G. Petrovskogo. 5, 217–272 (1979)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Kamynin, V.L.: Unique solvability of the inverse problem of determination of the leading coefficient in a parabolic equation. Diff. Equat. 47(1), 91–101 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Lyusternik, L.A., Sobolev, V.I.: Kratkii Kurs Functcional’nogo analiza (Brief Course of Functional Analysis). Vyssh. Shkola, Moscow (1982)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)MoscowRussia

Personalised recommendations