Geodesic
The inverse problem of recovering a leading coefficient in the two-dimensional heat equation
Matematičeskie zametki SVFU, Tome 24 (2017) no. 1, pp. 74-86 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the inverse problem of recovering a leading coefficient independent of one of the spatial variable $y$ in the two-dimensional heat equation. The overdetermination data is the values of the solution on the cross-section of the domain by the hyperplane $y=0$. The solution is sought in the class of functions whose Fourier image in the variable $y$ is compactly supported in the dual variable. Existence and uniqueness conditions of the solution to this problem in this class are established.
Keywords: inverse problem, overdetermination condition, second order parabolic equation, initial-boundary value problem. 
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B. N. Tsybikov. The inverse problem of recovering a leading coefficient in the two-dimensional heat equation. Matematičeskie zametki SVFU, Tome 24 (2017) no. 1, pp. 74-86. http://geodesic.mathdoc.fr/item/SVFU_2017_24_1_a6/

[1] Belov Ya. Ya., Inverse problems for parabolic equations, VSP, Utrecht, 2002 | MR

[2] Ivanchov M., Inverse problems for equation of parabolic type, Math. Stud. Monogr. Ser., 10, VNTL Publishers, Lviv, 2003, 238 pp. | MR

[3] Kozhanov A. I., Composite type equations and inverse problems, VSP, Utrecht, 1999 | MR | Zbl

[4] Isakov V., Inverse problems for partial differential equations, Appl. Math. Sci., 127, Springer Science Business Media, Berlin, 2006 | MR | Zbl

[5] Prilepko A. I., Orlovsky D. G., and Vasin I. A., Methods for solving inverse problems in mathematical physics, Marcel Dekker, New York, 1999 | MR

[6] Gol’dman N. L., “Properties of solutions of parabolic equations with unknown righs-hand side and adjoint problems”, Dokl. Math., 77:3 (2008), 350–355 | DOI | MR | Zbl

[7] Efremenkova O. B., “On solvability of one parabolic problem of determining the absorption coefficient of a special type”, Mat. Zamet. YaGU, 13:1 (2006), 72–79

[8] Pyatkov S. G. and Tsybikov B. N, “On evolutionary inverse problems for parabolic equations”, Dokl. Math., 77:1 (2008), 111-113 | DOI | MR | Zbl

[9] Pyatkov S. G. and Samkov M. L., “On some classes of coefficient inverse problems for parabolic systems of equations”, Sib. Adv. Math., 22:4 (2012), 287–302 | DOI | MR | Zbl

[10] Pyatkov S. G., “On some classes of inverse problems with overdetermination data on spacial manifolds”, Sib. Math. J., 57:5 (2016), 870–880 | DOI | MR | Zbl

[11] Pyatkov S. G. and Samkov M. L., “Solvability of some inverse problems for the nonstationary heat-and-mass-transfer system”, J. Math. Anal. Appl., 446:2 (2017), 1449–1465 | DOI | MR | Zbl

[12] Polyanin A. D., Handbook of Linear Equations of Mathematical Physics, Fizmatlit, Moscow, 2001

[13] Ladyzhenskaya O. A., Solonnikov V. A., and Ural’tseva N. N., Linear and quasi-linear equations of parabolic type, Transl. Math. Monogr., 23, Amer. Math. Soc., Providence, RI, 1968, 648 pp. | MR | Zbl