The Determination of a Parabolic Equation from Initial and Final Data
William Rundell · Proceedings of the American Mathematical Society · 1987
It is shown that an unknown, spatially-dependent coefficient $a(x)$ in the parabolic equation $ut - \Delta u + a(x)u = 0$ can be determined from a knowledge of both initial and final data. An existence and uniqueness theorem is given and the continuous dependence of the function $a(x)$ on the data is examined.