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Journal of Mathematical Sciences

, Volume 231, Issue 4, pp 558–571 | Cite as

A Nonlocal Inverse Problem for the Two-Dimensional Heat-Conduction Equation

  • N. Ye. Kinash
Article

We consider an inverse problem of determination of the time-dependent leading coefficient of a two-dimensional heat-conduction equation with nonlocal overdetermination condition. The existence and uniqueness conditions are established for the classical solution of the analyzed problem.

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References

  1. 1.
    I. B. Bereznyts’ka, “Inverse problem for a parabolic equation with nonlocal overdetermination condition,” Mat. Meth. Fiz.-Mekh. Polya, 44, No. 1, 54–62 (2001).MathSciNetGoogle Scholar
  2. 2.
    M. I. Ivanchov, Inverse Problems of Heat Conduction with Nonlocal Conditions, Preprint, Institute of Systems Studies of Education, Kiev (1995).Google Scholar
  3. 3.
    M. I. Ivanchov and R. V. Sahaidak, “Inverse problem of determination of the leading coefficient of a two-dimensional parabolic equation,” Mat. Meth. Fiz.-Mekh. Polya, 47, No. 1, 7–16 (2004).zbMATHGoogle Scholar
  4. 4.
    N. Ye. Kinash, “Inverse problem for a parabolic equation with nonlocal overdetermination condition,” Bukov. Mat. Zh., 3, No. 1, 64–73 (2015).MathSciNetzbMATHGoogle Scholar
  5. 5.
    A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover, New York (1999).zbMATHGoogle Scholar
  6. 6.
    O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type, AMS, Providence, RI (1968).CrossRefzbMATHGoogle Scholar
  7. 7.
    A. M. Nakhushev, Equations of Mathematical Biology [in Russian], Vysshaya Shkola, Nalchik (1995).zbMATHGoogle Scholar
  8. 8.
    A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Cliffs (1964).zbMATHGoogle Scholar
  9. 9.
    J. Chabrowski, “On nonlocal problems for parabolic equations,” Nagoya Math. J., 93, 109–131 (1984).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    C. Coles and D. A. Murio, “Identification of parameters in the 2D IHCP,” Comput. Math. Appl., 40, No. 8-9, 939–956 (2000).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    C. Coles and D. A. Murio, “Simultaneous space diffusivity and source term reconstruction in 2D IHCP,” Comput. Math. Appl., 42, No. 12, 1549–1564 (2001).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    W. A. Day, “Extensions of a property of the heat equation to linear thermoelasticity and other theories,” Quart. Appl. Math., 40, No. 3, 319–330 (1982).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    J. I. Diaz and J.-M. Rakotoson, “On a nonlocal stationary free-boundary problem arising in the confinement of a plasma in a Stellarator geometry,” J. Arch. Rat. Mech. Anal., 134, No. 1, 53–95 (1996).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    M. Ivanchov, “Inverse problems for equations of parabolic type,” in: Mathematical Studies: Monograph Series, Vol. 10, VNTL Publishers, Lviv (2003).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • N. Ye. Kinash
    • 1
  1. 1.I. Franko Lviv National UniversityLvivUkraine

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