Noemi David, Alpár R. Mészáros, Filippo Santambrogio
Published 2024-05-12Version 1
Nowadays a vast literature is available on the Hele-Shaw or incompressible limit for nonlinear degenerate diffusion equations. This problem has attracted a lot of attention due to its applications to tissue growth and crowd motion modelling as it constitutes a way to link soft congestion (or compressible) models to hard congestion (or incompressible) descriptions. In this paper, we address the question of estimating the rate of this asymptotics in the presence of external drifts. In particular, we provide improved results in the 2-Wasserstein distance which are global in time thanks to the contractivity property that holds for strictly convex potentials.
Convergence Rates and Hölder Estimates in Almost-Periodic Homogenization of Elliptic Systems
A Hele-Shaw limit without monotonicity
Sharp $L^1$-convergence rates to the Barenblatt solutions for the compressible Euler equations with time-varying damping
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