Uniqueness for coefficient identification in one-dimensional parabolic equations

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.