arXiv subjects

Elio Espejo

Publications and source records attributed to Elio Espejo.

2 recordsLinked to original sources

arXiv2026

Chemotaxis with tomography

Cells encounter a diverse array of physical and chemical signals as they navigate their natural surroundings. However, their response to the simultaneous presence of multiple cues remains elusive. Particularly, the impact of topography alongside a chemotactic gradient on cell migratory behavior remains insufficiently explored. In this paper, we investigate the effects of topographical obstacles during chemotaxis. Our approach involves modifying the Keller-Segel model, incorporating a spatially dependent coefficient of chemotaxis. Through our analysis, we demonstrate that this coefficient plays a crucial role in preventing blow-up phenomena in cell concentration.

math.AP↗

arXiv2024

Blow-up of solutions to the Keller-Segel model with tensorial flux in high dimensions

Over the course of the last decade, there has been a significant level of interest in the analysis of Keller-Segel models incorporating tensorial flux. Despite this interest, the question of whether finite-time blowup solutions exist remains a topic of ongoing research. Our study provides evidence that solutions of this nature are indeed possible in dimensions $n\geq3,$ when utilizing a tensorial flux expressed in the form of $A\nabla v$, where $A$ denotes a matrix with constant components

math.AP↗