Electron. J. Differential Equations, Vol. 2017 (2017), No. 07, pp. 1-7.

Uniqueness for coefficient identification in one-dimensional parabolic equations

Xuewen Wu, Guangsheng Wei

Abstract:
This article concerns the question of uniqueness in the identification of coefficients in a one-dimensional parabolic partial differential equation. The solution of an initial-boundary value problem is observed at one internal point over a finite time interval. It is shown that, under the condition that the coefficient is known a priori on a subinterval, the coefficient on the entire interval is uniquely determined by such observation.

Submitted May 12, 2016. Published January 10, 2017.
Math Subject Classifications: 35R30, 34A55, 34B24.
Key Words: Inverse problem; spectral data; parabolic equation.

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Xuewen Wu
College of Mathematics and Information Science
Shaanxi Normal University, Xi'an 710062, China
email: xuewenwu1991@163.com
Guangsheng Wei
College of Mathematics and Information Science
Shaanxi Normal University, Xi'an 710062, China
email: weimath@vip.sina.com

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