The inverse problem of finding the time-dependent diffusion coefficient of the heat equation from integral overdetermination data

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Kanca F., İSMAİLOV M.

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, vol.20, no.4, pp.463-476, 2012 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 20 Issue: 4
• Publication Date: 2012
• Doi Number: 10.1080/17415977.2011.629093
• Journal Name: INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.463-476
• Kocaeli University Affiliated: Yes

Abstract

This article considers the problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in one-dimensional heat equation in the case of nonlocal boundary and integral overdetermination conditions. The conditions for the existence and uniqueness of a classical solution of the problem under considerations are established. A numerical example using the Crank-Nicolson finite-difference scheme combined with an iteration method is presented and the sensitivity of this scheme with respect to noisy overdetermination data is illustrated.