The determination of a parabolic equation from initial and final data

Abstract

It is shown that an unknown, spatially-dependent coefficient a ( x ) a(x) in the parabolic equation u t − Δ u + a ( x ) u = 0 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 ) a(x) on the data is examined.