Geodesic
The Inverse Problem of Simultaneous Determination of the Two Lower Space-Dependent Coefficients in a Parabolic Equation
Matematičeskie zametki, Tome 106 (2019) no. 2, pp. 248-261.

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Existence and uniqueness theorems for the solution of the inverse problem of simultaneous determination of $x$-dependent coefficients at $u$ and $u_x$ in a nondivergent parabolic equation from integral observation are obtained. Estimates of the maximum absolute values of these coefficients with constants explicitly expressed via the input data of the problem are given. An example of an inverse problem to which the proved theorems apply is presented.
Keywords: inverse problems, integral observation
Mots-clés : parabolic equations. 
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V. L. Kamynin. The Inverse Problem of Simultaneous Determination of the Two Lower Space-Dependent Coefficients in a Parabolic Equation. Matematičeskie zametki, Tome 106 (2019) no. 2, pp. 248-261. http://geodesic.mathdoc.fr/item/MZM_2019_106_2_a7/

[1] N. V. Muzylev, “O edinstvennosti resheniya odnoi obratnoi zadachi nelineinoi teploprovodnosti”, Zh. vychisl. matem. i matem. fiz., 25:9 (1985), 1346–1352 | MR | Zbl

[2] N. I. Ivanchov, “Ob obratnoi zadache odnovremennogo opredeleniya koeffitsientov teploprovodnosti i teploemkosti”, Sib. matem. zhurn., 35:3 (1994), 612–621 | MR | Zbl

[3] Yu. E. Anikonov, Yu. Ya. Belov, “Determining two unknown coefficients of parabolic type equation”, J. Inverse Ill-Posed Probl., 9:5 (2000), 469–487 | DOI | MR

[4] N. I. Ivanchov, N. V. Pobyrivska, “Ob opredelenii dvukh zavisyaschikh ot vremeni koeffitsientov v parabolicheskom uravnenii”, Sib. matem. zhurn., 43:2 (2002), 406–413 | MR | Zbl

[5] Yu. Ya. Belov, S. V. Polyntseva, “Ob odnoi obratnoi zadache identifikatsii dvukh koeffitsientov mnogomernogo parabolicheskogo uravneniya”, Dokl. AN, 396:5 (2004), 583–586 | Zbl

[6] M. S. Hussein, D. Lesnic, M. I. Ivanchov, “Simultaneous determination of time-dependent coefficients in the heat equation”, Comput. Math. Appl., 67:5 (2014), 1065–1091 | DOI | MR | Zbl

[7] V. L. Kamynin, A. B. Kostin, “Obratnaya zadacha opredeleniya $n$ koeffitsientov pri mladshikh proizvodnykh v parabolicheskom uravnenii”, Differents. uravneniya, 50:4 (2014), 480–491 | DOI | Zbl

[8] V. L. Kamynin, “Obratnaya zadacha odnovremennogo opredeleniya pravoi chasti i koeffitsienta pered mladshei proizvodnoi v parabolicheskom uravnenii na ploskosti”, Differents. uravneniya, 50:8 (2014), 795–806 | DOI | Zbl

[9] V. L. Kamynin, “Obratnaya zadacha odnovremennogo opredeleniya pravoi chasti i mladshego koeffitsienta v parabolicheskom uravnenii so mnogimi prostranstvennymi peremennymi”, Matem. zametki, 97:3 (2015), 368–381 | DOI | MR | Zbl

[10] V. L. Kamynin, “Inverse problems of simultaneous determination of the time-dependent right-hand side term and the coefficient in a parabolic equation”, Finite Difference Methods, Theory and Applications, Lecture Notes in Comput. Sci., 9045, Springer, Cham, 2015, 218–225 | MR

[11] S. N. Kruzhkov, “Kvazilineinye parabolicheskie uravneniya i sistemy s dvumya nezavisimymi peremennymi”, Tr. sem. im. I. G. Petrovskogo, 5, 1979, 217–272 | Zbl

[12] S. N. Kruzhkov, Nelineinye uravneniya s chastnymi proizvodnymi, Ch. 1, Izd-vo Mosk. un-ta, M., 1969

[13] A. Fridman, Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, M., Nauka, 1968 | MR | Zbl

[14] D. Gilbarg, N. Trudinger, Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[15] L. A. Lyusternik, V. I. Sobolev, Kratkii kurs funktsionalnogo analiza, Vysshaya shkola, M., 1982 | MR