References
E. Hille and R. Phillips, Functional Analysis and Semigroups [Russian translation], IL, Moscow (1962).
A. I. Egorov, Optimal Control of Thermal and Diffusion Processes [in Russian], Nauka, Moscow (1978).
A.D. Iskenderov, “Inverse problems on determination of right sides of differential equations,” Izv. Akad. Nauk Azerb. SSR, No. 2, 58–63 (1976).
D. G. Orlovskii. “The problem of determining the parameters of evolution equations,” Differents. Uravn.,26, No. 9, 1614–1621 (1990).
Yu. S. Éidel'man, “Conditions for solvability of inverse problems for evolution equations,” Dokl. Akad. Nauk UkrSSR, Ser. A. No. 7, 28–31 (1990).
Yu. S. Éidel'man, “Inverse problems for parabolic and elliptic differential-operator equations,” Ukr. Mat. Zh.,45, No. 1, 120–127 (1993).
A. I. Prilepko and A. B. Kostin, “Inverse problems for parabolic equations with finite and integral observation,” Mat. Sbornik,183, No. 4, 49–68 (1992).
I. V. Tikhonov, “Inverse problems for evolution equations and applications to transfer equations,” Candidate's Dissertation, MIFN, 1993.
M. G. Krein, Linear Differential Equations in Banach Space [in Russian], Nauka, Moscow (1967).
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York (1983).
Yu. S. Éidel'man, “Correctness of forward and inverse problems for differential equations in Hilbert space,” Dokl. Ukr. Akad. Nauk, No. 12, 17–21 (1993).
P. E. Sobolevskii, “The theory of semigroups and stability of difference schemes,” in: The Theory of Operators in Functional Spaces [in Russian], Nauka, Novosibirsk (1977), pp. 304–337.
J. B. Baillon, “Charactère borné de certains générateurs de semigroupes lineaires dans les espaces de Banach,” C.R. Acad. Sci.290, Série A, 757–760 (1980).
C. C. Travis, “Differentiability of weak solutions to an abstract inhomogeneous differential equation,” Proc. Am. Math. Soc.,82, No. 3, 425–430 (1981).
G. F. Webb, “Regularity of solutions to an abstract inhomogeneous linear differential equation,” Proc. Am. Math. Soc.,62, No. 2, 271–277 (1977).
G. Greiner, J. Voigt, and M. Wolff, “On the spectral bound of the generator of semigroups of positive operators,” J. Operator Theory,5, No. 2, 245–256 (1981).
I. V. Tikhonov, “On the connections between inverse problems with finite and integral redefinitions,” Ukr. Mat. Nauk,47, No. 4, 211–212 (1992).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 56, No. 8, pp. 99–113, August 1994.
Rights and permissions
About this article
Cite this article
Tikhonov, I.V., Eidelman, Y.S. Problems on correctness of ordinary and inverse problems for evolutionary equations of a special form. Math Notes 56, 830–839 (1994). https://doi.org/10.1007/BF02110743
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02110743