We establish conditions for the unique solvability of the inverse problem of finding the lower coefficient with two unknown time-dependent parameters in a one-dimensional parabolic equation with integral overdetermination conditions in a domain with free boundary.
Similar content being viewed by others
References
Yin Hong-Ming, “Global solvability for some parabolic inverse problems,” J. Math. Anal. Appl., 392–403 (1991).
D. D. Trong and D. D. Ang, “Coefficient identification for a parabolic equation,” Inverse Problems, 10, No. 3, 733–752 (1994).
J. Cannon and S. Perez-Esteva, “Determination of the coefficient of u x in a linear parabolic equation,” Inverse Problems, 10, No. 3, 521–531 (1994).
M. I. Ivanchov and N. V. Pabyrivs’ka, “Simultaneous determination of two coefficients in a parabolic equation in the case of nonlocal and integral conditions,” Ukr. Mat. Zh., 53, No. 5, 589–596 (2001); English translation: Ukr. Math. J., 53, No. 5, 674–684 (2001).
N. V. Pabyrivs’ka, “Heat moments in inverse problems for parabolic equations,” Visn. Lviv. Univ., Ser. Mekh.-Mat., Issue 56, 142–149 (2000).
M. I. Ivanchov, “Inverse problem with free boundary for the heat equation,” Ukr. Mat. Zh., 55, No. 7, 901–910 (2003); English translation: Ukr. Math. J., 55, No. 7, 1086–1098 (2003).
I. Barans’ka, “Determination of the leading coefficient for a parabolic equation in a domain with unknown boundaries,” Visn. Lviv. Univ., Ser. Mekh.-Mat., Issue 64, 20–38 (2005).
H. A. Snitko, “Inverse problem for a parabolic equation in a domain with free boundary,” Mat. Met. Fiz.-Mekh. Polya, 50, No. 4, 7–18 (2007).
H. A. Snitko, “Inverse problem of determination of the lower coefficient for a parabolic equation in a domain with free boundary,” Visn. Nats. Univ “Lviv. Politekhn.” Fiz.-Mat. Nauk., Issue 643, 45–52 (2009).
H. A. Snitko, “Coefficient inverse problem for a parabolic equation in a domain with free boundary,” Mat. Met. Fiz.-Mekh. Polya, 51, No. 4, 37–47 (2008).
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Parabolic Equations [in Russian], Nauka, Moscow (1967).
M. Ivanchov, Inverse Problems for Equations of Parabolic Type, VNTL Publishers, Lviv (2003).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 11, pp. 1531–1549, November, 2013.
Rights and permissions
About this article
Cite this article
Snitko, H.A. Determination of the Lowest Coefficient for a One-Dimensional Parabolic Equation in a Domain with Free Boundary. Ukr Math J 65, 1698–1719 (2014). https://doi.org/10.1007/s11253-014-0890-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-014-0890-2