Calculus of Variations and Geometric Measure Theory
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F. Flei├čner

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

created by flei├čner on 12 Feb 2020

[BibTeX]

Submitted Paper

Inserted: 12 feb 2020
Last Updated: 12 feb 2020

Year: 2020

ArXiv: 2002.04496 PDF

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

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