Abstract
We establish conditions for the unique existence of a solution of the inverse problem of simultaneous determination of two unknown coefficients in a parabolic equation. One of these coefficients is the leading coefficient that depends on time, and the other coefficient depends on a space variable.
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A. D. Iskenderov, “On one inverse problem for a quasilinear parabolic equation,” Differents. Uravn., 10, No. 5, 890–898 (1974).
A. Ya. Akhundov. “Inverse problem for linear parabolic equations,” Dokl. Akad. Nauk Azer. SSR, 39, No. 5, 3–6 (1983).
N. V. Muzylev, “On the uniqueness of simultaneous determination of the coefficients of heat conductivity and bulk heat capacity,” Zh. Vych. Mat. Mat. Fiz., 23, No. 1, 102–108 (1983).
N. I. Ivanchov, “On the inverse problem of simultaneous determination of the coefficients of heat conductivity and heat capacity,” Sib. Mat. Zh., 35, No. 3, 612–621 (1994).
O. A. Ladyzhenskaya, V. A. Solonrukov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian] Nauka, Moscow 1967.
M. I. Ivanchov, Inverse Problems of Heat Conduction with Nonlocal Conditions [in Ukrainian] Preprint, Ministry of Education of Ukraine, Kiev 1995.
A. Friedman, Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs (1964).
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Ivanchov, M.I. Inverse problem of simultaneous determination of two coefficients in a parabolic equation. Ukr Math J 52, 379–387 (2000). https://doi.org/10.1007/BF02513132
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DOI: https://doi.org/10.1007/BF02513132