IDENTIFICATION OF Q(CHI) IN MU(T)=DELTA-MU-Q-MU FROM BOUNDARY OBSERVATIONS

We consider the problem of recovering the coefficient q(x) in the equa tion u(t) = Delta u - qu from boundary observations. Uniqueness of q b ased on knowledge of the Neumann --> Dirichlet response operator is sh own as an implication of (known) corresponding results concerning the inverse problem for the corresponding hyperbolic equation w(tt) = Delt a w - qw. This is then reduced to use of the response to a single inpu t with some consideration of computational approximation.