A Minimizing Movement approach to a class of scalar reaction-diffusion equations

Abstract: 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.