The author studies an inverse problem relative to the parabolic equation
The additional information is . Under certain conditions there is at most one solution pair (a,u) to the problem considered. It is a “folk-theorem” in undetermined coefficient problems that one gets a well-posed problem if the additional data is prescribed in a direction “parallel” to the coefficient but not if it is “perpendicular”. See also S. Handrock-Meyer, Inverse problems for the heat equation (German), to appear in Zeitschrift für Analysis und ihre Anwendungen.