  We consider initial boundary value problems with the homogeneous Neumann
boundary condition. Given an initial value, we establish the uniqueness in
determining a spatially varying coefficient of zeroth-order term by a single
measurement of Dirichlet data on an arbitrarily chosen subboundary. The
uniqueness holds in a subdomain where the initial value is positive, provided
that it is sufficiently smooth which is specified by decay rates of the Fourier
coefficients. The key idea is the reduction to an inverse elliptic problem and
relies on elliptic Carleman estimates.
