published on July 7, 2026
Boundary conditions and non kinematic free boundaries for wave-structure interactions
By David Lannes
Local sensing and nonlinear diffusion in models of chemotactic aggregation
Appears in collection : Mathematical models for proliferation and propagation / Modèles mathématiques pour la prolifération et la propagation
We consider a class of cross-diffusion systems modeling chemotactic aggregation by local sensing. While reminiscent of the classical (minimal) Keller-Segel system, which may exhibit blow-up in finite time, this class of system typically possesses global-in-time solutions. Using entropy and duality methods, we discuss their rich long-time behaviour. We also discuss possible extensions in presence of nonlinear self-diffusion.
