The Inverse Problem of the Simultaneous Determination of the Right-Hand Side and the Lowest Coefficient in Parabolic Equations with Many Space Variables
Matematičeskie zametki, Tome 97 (2015) no. 3, pp. 368-381.

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We obtain existence and uniqueness theorems for the solution of the inverse problem of the simultaneous determination of the right-hand side and the lowest coefficient in multidimensional parabolic equations with integral observation. We give an estimate of the maximum of the modulus of unknown coefficients with constants explicitly expressed in terms of the input data of the problem.
Mots-clés : multidimensional parabolic equation, Cordes condition
Keywords: inverse problem, maximum principle, Schauder fixed-point theorem.
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V. L. Kamynin. The Inverse Problem of the Simultaneous Determination of the Right-Hand Side and the Lowest Coefficient in Parabolic Equations with Many Space Variables. Matematičeskie zametki, Tome 97 (2015) no. 3, pp. 368-381. http://geodesic.mathdoc.fr/item/MZM_2015_97_3_a5/

[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 (2001), 469–487 | MR | Zbl

[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. RAN, 396:5 (2004), 583–586 | MR | Zbl

[6] V. L. Kamynin, “Obratnaya zadacha odnovremennogo opredeleniya pravoi chasti i koeffitsienta pered mladshei proizvodnoi v parabolicheskom uravnenii na ploskosti”, Differents. uravneniya, 50:6 (2014), 795–806

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

[8] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR | Zbl

[9] O. Arena, “Sopra una classe di equazioni paraboliche”, Boll. Un. Mat. Ital. (4), 2 (1969), 9–24 | MR | Zbl

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

[11] O. Arena, A. Maugeri, “Perturbazioni di operatori parabolici di ordine $2n$ con termini di ordine inferiore”, Boll. Un. Mat. Ital. (4), 9 (1974), 169–184 | MR | Zbl

[12] N. V. Krylov, Nelineinye ellipticheskie i parabolicheskie uravneniya vtorogo poryadka, Nauka, M., 1985 | MR | Zbl

[13] V. L. Kamynin, “Obratnaya zadacha opredeleniya mladshego koeffitsienta v parabolicheskom uravnenii pri uslovii integralnogo nablyudeniya”, Matem. zametki, 94:2 (2013), 207–217 | DOI | Zbl

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

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