  We consider a class of semilinear parabolic evolution equations subject to a
hysteresis operator and a Bochner-Lebesgue integrable source term. The
underlying spatial domain is allowed to have a very general boundary. In the
first part of the paper, we apply semigroup theory to prove well-posedness and
boundedness of the solution operator. Rate independence in reaction-diffusion
systems complicates the analysis, since the reaction term acts no longer local
in time. This demands careful estimates when working with semigroup methods. In
the second part, we show Lipschitz continuity and Hadamard differentiability of
the solution operator. We use fixed point arguments to derive a representation
for the derivative in terms of the evolution system. Finally, we apply our
results to an optimal control problem in which the source term acts as a
control function and show existence of an optimal solution.
