# IJPAM: Volume 113, No. 4 (2017)

# Title

AN INVERSE PROBLEM OF FINDINGTHE TIME-DEPENDENT HEAT TRANSFER

COEFFICIENT FROM AN INTEGRAL CONDITION

# Authors

Makhmud Sadybekov, Gulaiym Oralsyn, Mansur IsmailovInstitute 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

# Download Section

**Download paper from here.**

You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

## 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 . 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**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2017

**Volume:**113

**Issue:**4

**Pages:**139 - 149

Google Scholar; DOI (International DOI Foundation); WorldCAT.

**This work is licensed under the Creative Commons Attribution International License (CC BY).**