Geodesic
Inverse Problems of Finding the Absorption Parameter in the Diffusion Equation
Matematičeskie zametki, Tome 106 (2019) no. 3, pp. 395-408.

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The paper is devoted to the study of inverse problems of finding, together with a solution $u(x,t)$ of the diffusion equation $$ u_t-\Delta u +[c(x,t)+aq_0(x,t)]u=f(x,t), $$ the parameter $a$ characterizing absorption ($c(x,t)$ and $q_0(x,t)$ are given functions). It is assumed that, on the function $u(x,t)$, nonpercolation conditions and some special overdetermination conditions of integral form are imposed. We prove existence theorems for solutions $(u(x,t),a)$ such that the function $u(x,t)$ has all Sobolev generalized derivatives appearing in the equation and $a$ is a nonnegative number.
Mots-clés : diffusion equation, existence.
Keywords: nonpercolation condition, unknown parameter, inverse problems, final integral overdetermination conditions 
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A. I. Kozhanov. Inverse Problems of Finding the Absorption Parameter in the Diffusion Equation. Matematičeskie zametki, Tome 106 (2019) no. 3, pp. 395-408. http://geodesic.mathdoc.fr/item/MZM_2019_106_3_a6/

[1] V. S. Vladimirov, Uravneniya matematicheskoi fiziki, Nauka, M., 1988 | MR | Zbl

[2] A. Lorenzi, “Recovering two constants in a linear parabolic equation”, J. Phys.: Conf. Ser., 73 (2007), 012014 | DOI

[3] A. Lorenzi, G. Mola, “Identification of a real constant in linear evolution equation in a Hilbert spaces”, Inverse Probl. Imaging, 5:3 (2011), 695–714 | DOI | MR

[4] G. Mola, “Identification of the diffusion coefficient in linear evolution equation in a Hilbert spaces”, J. Abstr. Differ. Equ. Appl., 2:1 (2011), 14–28 | MR

[5] A. Lorenzi, G. Mola, “Recovering the reaction and the diffusion coefficients in a linear parabolic equations”, Inverse Problems, 28:7 (2012), 075006 | DOI | MR

[6] A. Lorenzi, E. Paparoni, “Identifications of two unknown coefficients in an integro-differential hyperbolic equation”, J. Inverse Ill-Posed Probl., 1:4 (1993), 331–348 | MR

[7] A. S. Lyubanova, “Identification of a constant coefficient in an elliptic equation”, Appl. Anal., 87:10-11 (2008), 1121–1128 | DOI | MR

[8] A. I. Kozhanov, R. R. Safiullova, “Opredelenie parametrov v telegrafnom uravnenii”, Ufimsk. matem. zhurn., 9:1 (2017), 63–74

[9] A. I. Kozhanov, “Nelineinye nagruzhennye uravneniya i obratnye zadachi”, Zh. vychisl. matem. i matem. fiz., 44:4 (2004), 694–716 | MR | Zbl

[10] A. I. Kozhanov, “Parabolicheskie uravneniya s neizvestnymi koeffitsientami, zavisyaschimi ot vremeni”, Zh. vychisl. matem. i matem. fiz., 57:6 (2017), 961–972 | DOI | MR

[11] M. T. Dzhenaliev, K teorii lineinykh kraevykh zadach dlya nagruzhennykh differentsialnykh uravnenii, In-t teor. i prikl. matem., Almaty, 1995

[12] A. M. Nakhushev, Nagruzhennye uravneniya i ikh primenenie, Nauka, M., 2012

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

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

[15] V. A. Trenogin, Funktsionalnyi analiz, Nauka, M., 1980 | MR

[16] S. L. Sobolev, Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR | Zbl