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 
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/
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[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