THE DETERMINATION OF A COEFFICIENT IN A PARABOLIC EQUATION FROM INPUTSOURCES

The authors consider the question of recovering the coefficient q from the equation u(t) - u(xx) + q(x)u = f(i)(x) with homogeneous initial and boundary conditions. The nonhomogeneous source terms {f(j)(x)}j=1i nfinity form a basis for L2(0, 1). It is proved that a unique determin ation is possible from data measurements consisting of either the flux at one end of the bar or the net flux leaving the bar, taken at a sin gle fixed time for each input source. An algorithm that allows efficie nt numerical reconstruction of q(x) from finite data is given.