On a counterexample of inverse parabolic problems with final overdetermination
The author states that \textit{V. Isakov}'s counterexample [Commun. Pure Appl. Math. 44, No. 2, 185--209 (1991; Zbl 0729.35146)] on the existence of a function \(\alpha\) with certain properties for which the uniqueness of a solution to the inverse problem of determining the function \(f(x)\) from the system \(u_t - u_{xx} = \alpha(x,t)f(x), (x,t) \in (0,1)\times (0,T), u(0,t) = u(1,t) = 0, 0 < t \leq T, u(x,0) = 0, u(x,T) = 0, 0 \leq x \leq 1\) fails.
scientific article; zbMATH DE number 6336242