On nonlinear cross-diffusion systems: an optimal transport approach |
| |
Authors: | Inwon?Kim Email author" target="_blank">Alpár?Richárd?MészárosEmail author |
| |
Institution: | 1.Department of Mathematics,UCLA,Los Angeles,USA |
| |
Abstract: | We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of discrete-time solutions. Its continuum limit, due to the possible mixing of the densities, only solves a weaker version of the original system. In one space dimension, we find a stable initial configuration which allows the densities to be segregated. This leads to the evolution of a stable interface between the two densities, and to a stronger convergence result to the continuum limit. In particular derivation of a standard weak solution to the system is available. We also study the incompressible limit of the system, which addresses transport under a height constraint on the total density. In one space dimension we show that the problem leads to a two-phase Hele-Shaw type flow. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|