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

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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> n-1 spatial variables. For the Schrödinger equation, we assume that a potential depends on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> n-1 spatial variables. The data are taken on a part of the boundary satisfying some geometric condition.