Mathematical Review of MR265 0574 "An error estimate for an approximate solution of an inverse problem for a parabolic equation. (Russian)" by Tanana, V. P.; Kolesnikova, N. Yu

An apparently "innocuous'' problem derived from the heat equation, namely the determination of the boundary values $u(1,t)$ of the function $u(\cdot,\cdot)$ which satisfies $$ \partial_t u(x,t) =\partial^2_{xx}u(x,t)+a(x)u(x,t),\quad x\in (0,1),\ t\ge 0,\tag1 $$,(1) $$ \gathered u(x,0) = 0,\ x\in [0,1],\quad u(0,t) = 0,\ t\ge 0,\\ u(x_0,t) = f(t),\ 0< x_0 < 1,\ t\ge 0,\endgathered \tag2$$,(2) from knowledge of $a(\cdot)\in {\scr C}^2 ([0,1])$ and $f(\cdot)$, gives rise to a logarithmic estimate for an "approximate solution'' $u_{\delta}(1,t)$, $t\ge 0$.