2022/08/31 by Simone Di Marino, Di Marino, Simone, Lorenzo Portinale +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2208.14753
openalex publication_date 2022/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the discretization of generalized Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of deterministic particle approximation of partial differential equations. In particular, we provide a Γ-convergence result for the associated discrete metrics as N → ∞ to the continuous one and discuss applications to the approximation of one-dimensional conservation laws (of gradient flow type) via the so-called generalized minimizing movements, proving a convergence result of the schemes at any given discrete time step τ>0. This the first work of a series aimed at shedding new lights on the interplay between generalized gradient-flow structures, conservation laws, and Wasserstein distances with nonlinear mobilities.