3 papers
math.AP2025
A Li-Yau and Aronson-Bénilan approach for the Keller-Segel system with critical exponent
Charles Elbar, Alejandro Fernández-Jiménez, Filippo Santambrogio
We prove Li-Yau and Aronson-Bénilan type estimates for the parabolic-elliptic Keller-Segel system with critical exponent , i.e. lower bounds on the Laplacian of a su…
math.AP2025
A deterministic particle approximation for a fourth-order equation
Charles Elbar, Alejandro Fernández-Jiménez
We provide a deterministic particle approximation to a fourth order equation with applications in cell-cell adhesion. In order to do that, first we show that the equation can be as…
math.AP2025
Drift-diffusion equations with saturation
José Antonio Carrillo, Alejandro Fernández-Jiménez, David Gómez-Castro
We focus on a family of nonlinear continuity equations for the evolution of a non-negative density with a continuous and compactly supported nonlinear mobility $\mathrm{m}(Ï)…