7 citations · 10 across the 5 of their papers we have counts for
7 papers
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…
Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts
Luca Alasio, Maria Bruna, Simone Fagioli +1
We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate-parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interac…
Trend to Equilibrium for Systems with Small Cross-Diffusion
Luca Alasio, Helene Ranetbauer, Markus Schmidtchen +1
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynam…
Global existence for a class of viscous systems of conservation laws
Luca Alasio, Stefano Marchesani
We prove existence and boundedness of classical solutions for a family of viscous conservation laws in one space dimension for arbitrarily large time. The result relies on H. Amann…
The role of a strong confining potential in a nonlinear Fokker-Planck equation
Luca Alasio, Maria Bruna, José Antonio Carrillo
We show that solutions of nonlinear nonlocal Fokker--Planck equations in a bounded domain with no-flux boundary conditions can be approximated by Cauchy problems with increasingly…