Determination of source terms and coefficients dependent on <i>n</i> - 1 spatial variables of parabolic and Schrödinger equations

Abstract We establish the uniqueness in the determination of a source term or a coefficient of the zeroth order term of a second-order parabolic equation. Moreover, we consider the determination of a potential of the Schrödinger equation. For a parabolic equation, an unknown source term and an unknown coefficient depend on the time and n - 1 n-1 spatial variables. For the Schrödinger equation, we assume that a potential depends on n - 1 n-1 spatial variables. The data are taken on a part of the boundary satisfying some geometric condition.