Literature Cited
A. N. Tikhonov, “Uniqueness theorems for the heat condition equation,” Matem. Sb.,42, No. 2, 199–216 (1935).
A. I. Prilepko, “On certain integral equations of the first kind for inverse problems,” in: The Application of Function Methods to Differential Equations [in Russian], Novosibirsk (1972), pp. 199–205.
M. M. Lavrent'ev, “On a class of inverse problems for differential equations,” Dokl. Akad. Nauk SSSR,160, No. 1, 32–35 (1965).
M. M. Lavrent'ev and K. G. Reznitskaya, “Uniqueness theorems for certain nonlinear inverse problems for equations of parabolic type,”, Dokl. Akad. Nauk SSSR,208, No. 3, 531–532 (1973).
M. M. Lavrent'ev, V. G. Romanov, and V. G. Vasil'ev, Multidimensional Inverse Problems for Differential Equations [in Russian], Nauka, Novosibirsk (1969).
B. M. Budak and A. D. Iskenderov, “A class of boundary-value problems with unknown coefficients,” Dokl. Akad. Nauk SSSR,175, No. 1, 13–16 (1967).
B. M. Budak and A. D. Iskenderov “A class of inverse boundary-value problems with unknown coefficients,” Dokl. Akad. Nauk SSSR,176, No. 1, 20–23 (1967).
A. I. Prilepko, “Inverse problems in potential theory (elliptic, parabolic, and hyperbolic equations, and the transport equation),” Matem. Zametki,14, No. 5, 755–767 (1973).
V. G. Romanov, Inverse Problems for Differential Equations. Specialist course for students of Novosibirsk State University [in Russian], Novosibirsk Univ., Novosibirsk (1973).
N. Ya. Beznoschenko, “The determination of the coefficients of the lower order terms in a parabolic equation,” Sibirsk. Matem. Zh.,16, No. 3, 473–482 (1975).
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).
G. N. Polozhii, Equations of Mathematical Physics [in Russian], Vysshaya Shkola, Moscow (1964).
S. C. Chu and F. T. Metcalf, “On Gronwall's inequality,” Proc. Amer. Math. Soc.,18, No. 3, 439–440 (1967).
A. M. Il'in, A. S. Kalashnikov, and O. A. Oleinik, “Second-order linear equations of parabolic type,” Usp. Matem. Nauk,17, No. 3, 3–146 (1962).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 16, No. 6, pp. 1135–1147, November–December, 1975.
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Beznoshchenko, N.Y. Some problems in determining the lower-order-term coefficients in parabolic equations. Sib Math J 16, 869–878 (1975). https://doi.org/10.1007/BF00967382
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DOI: https://doi.org/10.1007/BF00967382