The Inverse Problem of Determining the Lower-Order Coefficient in Parabolic Equations with Integral Observation
Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 207-217.

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Existence and uniqueness theorems for the solution to the inverse problem of determining the lower-order coefficient in multidimensional parabolic equations with integral observation are obtained. An estimate of the maximum of the modulus of the unknown coefficient with a constant explicitly expressed via the input data of the problem is given.
Mots-clés : multidimensional parabolic equation, Cordes-type condition.
Keywords: inverse problem for parabolic equations with integral observation, maximum principle
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V. L. Kamynin. The Inverse Problem of Determining the Lower-Order Coefficient in Parabolic Equations with Integral Observation. Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 207-217. http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a4/

[1] A. I. Prilepko, A. B. Kostin, “Ob obratnykh zadachakh opredeleniya koeffitsienta v parabolicheskom uravnenii. I”, Sib. matem. zhurn., 33:3 (1992), 146–155 | MR | Zbl

[2] A. I. Prilepko, A. B. Kostin, “Ob obratnykh zadachakh opredeleniya koeffitsienta v parabolicheskom uravnenii. II”, Sib. matem. zhurn., 34:5 (1993), 147–162 | MR | Zbl

[3] A. I. Prilepko, I. V. Tikhonov, “Printsip pozitivnosti resheniya v lineinoi obratnoi zadache i ego primenenie k koeffitsientnoi zadache teploprovodnosti”, DAN, 394:1 (1999), 21–23 | MR | Zbl

[4] A. I. Kozhanov, “Ob odnom nelineinom nagruzhennom parabolicheskom uravnenii i o svyazannoi s nim obratnoi zadache”, Matem. zametki, 76:6 (2004), 840–853 | DOI | MR | Zbl

[5] V. L. Kamynin, A. B. Kostin, “Dve obratnye zadachi opredeleniya koeffitsienta v parabolicheskom uravnenii”, Differents. uravneniya, 46:3 (2010), 372–383 | MR | Zbl

[6] V. L. Kamynin, T. I. Bukharova, “Obratnaya zadacha opredeleniya koeffitsienta pogloscheniya v parabolicheskom uravnenii na ploskosti”, Vestn. RUDN. Ser. Matem., fiz., inform., 2011, no. 2, 5–15

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

[8] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967 | MR | Zbl

[9] O. Arena, “Sopra una classe di equazioni paraboliche”, Boll. Un. Mat. Ital. (4), 2:1 (1969), 9–24 | MR | Zbl

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

[11] G. Talenti, “Sopra una classe di equazioni ellittiche a coefficienti misurabili”, Ann. Mat. Pura Appl. (4), 69 (1969), 285–304 | DOI | MR | Zbl

[12] M. Chicco, “Principio di massimo per soluzioni di equazioni ellitiche del secondo ordine di tipo Cordes”, Ann. Mat. Pura Appl. (4), 100 (1974), 239–258 | DOI | MR | Zbl

[13] 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

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

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

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

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