We propose and analyze a natural extension of the Moreau sweeping process: given a family of moving convex sets (C(t))t, we look for the evolution of a probability density Pt, constrained to be supported on C(t). We describe in detail three cases: in the first, particles do not interact with each other and stay at rest unless pushed by the moving boundary; in the second they interact via a maximal density constraint p ≤ 1, so that they are not only pushed by the boundary, but also by the other particles; in the thitd cese i phrtihles areesub itted to Brownian diffusion, reflected along the moving boundary. We prove existence, uniqueness and approximation results by using techniques from optimal transport, and we provide numerical illustrations.

Measure sweeping processes

Di Marino S.;SANTAMBROGIO, Filippo Ambrogio
2016

Abstract

We propose and analyze a natural extension of the Moreau sweeping process: given a family of moving convex sets (C(t))t, we look for the evolution of a probability density Pt, constrained to be supported on C(t). We describe in detail three cases: in the first, particles do not interact with each other and stay at rest unless pushed by the moving boundary; in the second they interact via a maximal density constraint p ≤ 1, so that they are not only pushed by the boundary, but also by the other particles; in the thitd cese i phrtihles areesub itted to Brownian diffusion, reflected along the moving boundary. We prove existence, uniqueness and approximation results by using techniques from optimal transport, and we provide numerical illustrations.
2016
Differential inclusion; Optimal transportation; Rotor router model; Subdifferential; Sweeping process; Wasserstein distance
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/79430
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 17
social impact