zbMATH — the first resource for mathematics

The inverse problem of the simultaneous determination of the right-hand side and the lowest coefficient in parabolic equations with many space variables. (English. Russian original) Zbl 1325.35281
Math. Notes 97, No. 3, 349-361 (2015); translation from Mat. Zametki 97, No. 3, 368-381 (2015).
Summary: 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 inmultidimensional 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.

35R30 Inverse problems for PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
Full Text: DOI
[1] Muzylev, N. V., On uniqueness of the solution of an inverse problem of nonlinear heat conduction, Zh. Vychisl. Mat. i Mat. Fiz., 25, 1346-1352, (1985) · Zbl 0589.35089
[2] Ivanchov, N. I., On the inverse problem of simultaneous determination of thermal conductivity and specific heat capacity, Sibirsk. Mat. Zh., 35, 612-621, (1994) · Zbl 0860.35143
[3] Anikonov, Y.u. E.; Belov, Y.u. Y.a., Determining two unknown coefficients of parabolic type equation, J. Inverse Ill-Posed Probl., 9, 469-487, (2001) · Zbl 0992.35113
[4] Ivanchov, N. I.; Pobyrivska, N. V., On determination of two time-dependent coefficients in a parabolic equation, Sibirsk. Mat. Zh., 43, 406-413, (2002) · Zbl 1007.35099
[5] Belov, Y.u. Y.a.; Polyntseva, S. V., On the problem of identification of two many-dimensional parabolic equation coefficients, Dokl. Ross. Akad. Nauk, 396, 583-586, (2004)
[6] Kamynin, V. L., The inverse problem of the simultaneous determination of the right-hand side and the coefficient of the lower derivative in parabolic equations on the plane, Differ. Uravn., 50, 795-806, (2014)
[7] A. Fridman, Partial Differential Equations of Parabolic Type (Moscow, Nauka, 1968) [in Russian].
[8] O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Equations of Elliptic Type (Nauka, Moscow, 1973) [in Russian]. · Zbl 0269.35029
[9] Arena, O., Sopra una classe di equazioni paraboliche, Boll. Un.Mat. Ital, 2, 9-24, (1969) · Zbl 0174.42201
[10] S. N. Kruzhkov, Nonlinear Partial Differential Equations (Izd. Moskov. Univ., Moscow, 1969), Vol. 1 [in Russian]. · Zbl 1007.35099
[11] Arena, O.; Maugeri, A., Perturbazioni di operatori parabolici di ordine 2\(n\) con termini di ordine inferiore, Boll. Un.Mat. Ital, 9, 169-184, (1974) · Zbl 0291.35045
[12] N. V. Krylov, Nonlinear Elliptic and Parabolic Equations of Second Order (Nauka, Moscow, 1985) [in Russian]. · Zbl 0586.35002
[13] Kamynin, V. L., The inverse problem of determining the low-order coefficient in parabolic equations with integral observation, Mat. Zametki, 94, 207-217, (2013)
[14] Kruzhkov, S. N., Quasilinear parabolic equations and systems with two independent variables, Trudy Sem. Petrovsk, 5, 217-272, (1979) · Zbl 0434.35058
[15] L. A. Lyusternik and V. I. Sobolev, A Short Course in Functional Analysis (Vyssh. Shkola, Moscow, 1982) [in Russian].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.