Calculus of Variations and Geometric Measure Theory

S. Fagioli - E. Radici

Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation

created by radici on 30 Jan 2018
modified on 28 Oct 2022


Published Paper

Inserted: 30 jan 2018
Last Updated: 28 oct 2022

Journal: Math. Mod. Meth. in Appl. Sci.
Year: 2018

ArXiv: 1801.10114 PDF


We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to nonnegative initial data in $L^{\infty} \cap BV$ away from vacuum and supported in a closed interval with zero-velocity boundary conditions. The main novelties of this work concern the presence of a nonlinear mobility term and the non strict monotonicity of the diffusion function. As a consequence, our result applies also to strongly degenerate diffusion equations. The conclusions are complemented with some numerical simulations.