Inserted: 12 feb 2020
Last Updated: 2 sep 2021
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.
Keywords: Optimal transport, Gradient flows, minimizing movements, reaction-diffusion equations, Hellinger-Kantorovich distance