Volume 27, 2021
|Number of page(s)||29|
|Published online||22 March 2021|
A minimizing Movement approach to a class of scalar reaction–diffusion equations
Technische Universität München,
* Corresponding author: email@example.com
Accepted: 15 December 2020
which is built on their gradient-flow-like structure in the space of finite nonnegative Radon measures on , endowed with the recently introduced Hellinger-Kantorovich distance HKΛ,Σ. It is proved that, under natural general assumptions on and , the Minimizing Movement scheme
yields weak solutions to the above equation as the discrete time step size τ ↓ 0. Moreover, a superdifferentiability property of the Hellinger-Kantorovich distance HKΛ,Σ, which will play an important role in this context, is established in the general setting of a separable Hilbert space; that result will constitute a starting point for the study of the differentiability of HKΛ,Σ along absolutely continuous curves which will be carried out in a subsequent paper.
Mathematics Subject Classification: 35K57 / 35K20 / 35K55 / 49M25 / 47J25 / 47J30 / 28A33 / 54E35 / 46G99 / 49Q20
Key words: Optimal transport / gradient flows / Minimizing Movements / reactiondiffusion equations / Hellinger-Kantorovich distance
© EDP Sciences, SMAI 2021
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