6 papers
Instantaneous regularisation via Harnack-type methods for a degenerate non-local equation
Simon M. Schulz
We prove an instantaneous smoothing effect for a degenerate non-local evolution equation (originally derived as the many-particle limit of a system of active Brownian particles). T…
Segregated solutions of a degenerate cross-diffusion system with drifts
Filippo Santambrogio, Simon Schulz
We prove the global existence of segregated weak solutions of a one-dimensional degenerate cross-diffusion system with independent drifts, which is endowed with a Wasserstein gradi…
Regularity and Uniqueness for a Model of Active Particles with Angle-Averaged Diffusions
Luca Alasio, Simon Schulz
We study the regularity and uniqueness of weak solutions of a degenerate parabolic equation, arising as the limit of a stochastic lattice model of self-propelled particles. The ang…
Regularity and trend to equilibrium for a non-local advection-diffusion model of active particles
Luca Alasio, Jessica Guerand, Simon Schulz
We establish regularity and, under suitable assumptions, convergence to stationary states for weak solutions of a parabolic equation with a non-linear non-local drift term; this eq…
Well-posedness and stationary states for a crowded active Brownian system with size-exclusion
Martin Burger, Simon Schulz
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle sys…
Phase Separation in Systems of Interacting Active Brownian Particles
M. Bruna, M. Burger, A. Esposito +1
The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present f…