5 papers · 1 filter
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…