  The purpose of this paper is to introduce a Minimizing Movement approach to a
class of scalar reaction-diffusion equations, which is built on their
gradient-flow-like structure in the space of finite nonnegative Radon measures,
endowed with the recently introduced Hellinger-Kantorovich distance. Moreover,
a superdifferentiability property of the Hellinger-Kantorovich distance, which
will play an important role in this context, is established in the general
setting of a separable Hilbert space.
