Published Paper

Inserted: 12 feb 2020
Last Updated: 2 sep 2021

Journal: ESAIM:COCV
Year: 2020
Doi: https://doi.org/10.1051/cocv/2020090

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.

Keywords: Optimal transport, Gradient flows, minimizing movements, reaction-diffusion equations, Hellinger-Kantorovich distance