An inverse problem for the heat equation

Abstract

Let ut = uxx - q(x)u, 0 ≤ × ≤ 1, t > 0, u(0, t) = 0, u(1, t) = a(t), u(x, 0) = 0, where a(t) is a given function vanishing for t > T, a(t) ≢ 0, ∫0T a(t)dt 0. Does this information determine q(x) uniquely? Do the measurements of the flux ux(1, t) := b(t) give more information about q(x) than b0(t) does? These questions are answered in this note. © 2001 Elsevier Science.