Abstract
In this paper we consider an inverse problem for the differential equationu t =u xx +q(x, t) u; the problem amounts to finding the coefficient q(x, t) from the solution of a series of Cauchy problems for this equation, the solution being specified on some manifold. Our main result is a proof of a uniqueness theorem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Vol. 23, American Math. Soc. Translation, Providence, R. I. (1968).
V. G. Romanov, “An abstract inverse problem and questions concerning its correctness,” Funktsional'. Analiz i Ego Prilozhen.,7, No. 3, 67–74 (1973).
V. G. Romanov, “On a theorem of uniqueness for a problem of integral geometry on a family of curves,” in: Mathematical Problems of Geophysics [in Russian], No. 4, Nauka, Novosibirsk (1973), pp. 140–146.
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 595–600, April, 1976.
Rights and permissions
About this article
Cite this article
Romanov, V.G. An inverse problem for an equation of parabolic type. Mathematical Notes of the Academy of Sciences of the USSR 19, 360–363 (1976). https://doi.org/10.1007/BF01156798
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01156798