A quasilinear Keller-Segel model with saturated discontinuous advection
Abstract
We consider the singular limit of a chemotaxis model of bacterial collective motion recently introduced in arXiv:2009.11048 [math.AP]. The equation models aggregation-diffusion phenomena with advection that is discontinuous and depends sharply on the gradient of the density itself. The quasi-linearity of the problem poses major challenges in the construction of the solution and complications arise in the proof of regularity. Our method overcomes these obstacle by relying solely on entropy inequalities and the theory of monotone operators. We provide existence, uniqueness and smoothing estimates in any dimensional space.
Fields of Study & Subjects
Mathematical Biology Tumor Growth
advanced mathematical theories
MRI in cancer diagnosis
Publication details
- Journal / source
- Communications in Partial Differential Equations
- Publisher
- Informa UK Limited
- Volume
- 51
- Issue
- 2-3
- Pages
- 99–130
- Publication date
- 4 March 2026
- Language
- EN