  We consider the inverse problem of determining a general semilinear term
appearing in nonlinear parabolic equations. For this purpose, we derive a new
criterion that allows to prove global recovery of some general class of
semilinear terms from lateral boundary measurements of solutions of the
equation with initial condition fixed at zero. More precisely, we prove, for
what seems to be the first time, the unique and stable recovery of general
semilinear terms depending on time and space variables independently of the
solution of the nonlinear equation from the knowledge of the parabolic
Dirichlet-to-Neumann map associated with the solution of the equation with
initial condition fixed at zero. Our approach is based on the second
linearization of the inverse problem under consideration.
