We establish the conditions for the existence and uniqueness of a smooth solution to the inverse problem for the two-dimensional heat equation with unknown leading coefficient depending on time and the space variable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. G. Savateev, “On the problem of identification of coefficient in a parabolic equation,” Sib. Mat. Zh., 36, No. 1, 177–185 (1995).
M. I. Ivantchov, “Determination simultanee de deux coefficients aux variables diverses dans une equation parabolique,” Mat. Stud., 10, No. 2, 173–187 (1998).
M. Ivanchov, Inverse Problems for Equations of Parabolic Type, VNTL Publishers, Lviv (2003).
N. Ya. Beznoshchenko, “On the existence of solutions in the problems of determination of coefficients at higher derivatives for parabolic equations,” Differents. Uravn., 18, No. 6, 996–1000 (1982).
N. Ya. Beznoshchenko, “Sufficient conditions for the existence of solutions of the problems of determination of coefficients at higher derivatives for a parabolic equation,” Differents. Uravn., 19, No. 11, 1908–1915 (1983).
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs (1964).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 12, pp. 1605–1614, December, 2017.
Rights and permissions
About this article
Cite this article
Ivanchov, M.I., Kinash, N.E. Inverse Problem for the Heat-Conduction Equation in a Rectangular Domain. Ukr Math J 69, 1865–1876 (2018). https://doi.org/10.1007/s11253-018-1476-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-018-1476-1