  This paper considers the inverse problem of recovering both the unknown,
spatially-dependent conductivity $a(x)$ and the nonlinear reaction term $f(u)$
in a reaction-diffusion equation from overposed data. These measurements can
consist of: the value of two different solution measurements taken at a later
time $T$; time-trace profiles from two solutions; or both final time and
time-trace measurements from a single forwards solve data run. We prove both
uniqueness results and the convergence of iteration schemes designed to recover
these coefficients. The last section of the paper shows numerical
reconstructions based on these algorithms.
