# 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

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# 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

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