AN INVERSE PROBLEM OF FINDING THE TIME-DEPENDENT HEAT TRANSFER COEFFICIENT FROM AN INTEGRAL CONDITION

M. Sadybekov, G. Oralsyn, M. Ismailov

IJPAM: Volume 113, No. 4 (2017)

Title

AN INVERSE PROBLEM OF FINDING
THE TIME-DEPENDENT HEAT TRANSFER
COEFFICIENT FROM AN INTEGRAL CONDITION

Authors

Makhmud Sadybekov

, Gulaiym Oralsyn

, Mansur Ismailov

$^{1,2}$ Institute of Mathematics and Mathematical Modeling
Almaty, KAZAKHSTAN

Al-Farabi Kazakh National University
Almaty, KAZAKHSTAN

Gebze Technical University
Gebze, TURKEY

Abstract

We consider the inverse problem of determining the time-dependent diffusivity in one-dimensional heat equation with periodic boundary conditions and nonlocal over-specified data. The problem is highly nonlinear and it serves as a mathematical model for the technological process of external guttering applied in cleaning admixtures from silicon chips. The well-posedness conditions for the existence, uniqueness and continuous dependence upon the data of the classical solution of the problem are established.

History

Received: December 15, 2016
Revised: January 30, 2017
Published: March 30, 2017

AMS Classification, Key Words

AMS Subject Classification: 35K15, 35P10, 35R30
Key Words and Phrases: heat transfer, heat equation, inverse problem, thermal diffusivity, integral condition

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Bibliography

1: M.I. Ismailov, F. Kanca, The inverse problem of finding thetime-dependent diffusion coefficient of the heat equation fromintegral overdetermination data, Inverse Problems in Scienceand Engineering, 20 (2012), 463-476.
2: M.I. Ivanchov, Some inverseproblems for the heat equation with nonlocal boundary conditions,Ukrainian Mathematical Journal, 45 (1994),1186-1192.
3: F. Kanca, Inverse coefficient problem of the parabolic equationwith periodic boundary and integral overdetermination conditions,Abstract and Applied Analysis, 2013 (2013),Article ID659804, 7 pages.
4: D. Lesnic, S.A. Yousefi, M. Ivanchov, Determination of atime-dependent diffusivity form nonlocal conditions, Journalof Applied Mathematics and Computation, 41 (2013),301-320.
5: S.A. Yousefi, D. Lesnic, Z. Barikbin, Satisfier function inRitz-Galerkin method for the identification of a time-dependentdiffusivity, Journal of Inverse and Ill-Posed Problems,20 (2012), 701-722.
6: G.K. Namazov, Inverse Problems of the Theory of Equations ofMathematical Physics, Baku, Azerbaijan (1984) (in Russian).
7: L.A. Muravei, V.M. Petrov, Some problems of control of diffusiontechological process, Current Problems of Modelling andControl of System with Distributed Parameters, Kiev (1987),42-43 (in Russian).
8: L.A. Muravei, A.V. Filinovskii, On a problem with nonlocalboundary condition for a parabolic equation, Mathematics ofthe USSR-Sbornik, 74 (1993), 219-249.
9: M.S. Hussein, D. Lesnic, M.I. Ismailov,An inverse problem of finding the time-dependent diffusioncoefficient from an integral condition, Math. Meth. Appl.Sci., 39 (2016), 963-980.
10: M.I. Ismailov, F. Kanca, An inverse coefficient problem for aparabolic equation in the case of nonlocal boundary andoverdetermination conditions, Mathematical Methods in theApplied Sciences, 34 (2011), 692-702.
11: Ionkin NI. Solution of a boundary-value problem in heatconduction with a nonclassical boundary condition, Equations, 13 (1977) 204-211.
12: M.A. Sadybekov, A.M. Sarsenbi, On thetheory of antiprior estimates in the sense of VA Il�in, Mathematics, 77, No. 3 (2008), 398-400.
13: M.A. Sadybekov, A.M. Sarsenbi, The use ofanti-A priori estimates in the theory of bases in the space L(2),Differential Equations, 44, No. 5 (2008), 685-�691.
14: P. Lang, J. Locker, Spectral theory of two-pointdifferential operators determined by $D^{2}$ . II. Analysis ofcase, J. Math. An. Appl., 146, No. 1 (1990),148-191.
15: M. Sadybekov, G. Oralsyn, M. Ismailov, An inverse problem offinding the time-dependent heat transfer coefficient from anintegral condition, Kazakh Mathematical Journal,17, No. 1 (2017), 47-48.

How to Cite?

DOI: 10.12732/ijpam.v113i4.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 4
Pages: 139 - 149

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