Work

A Kinetic Chemotaxis Model and Its Diffusion Limit in Slab Geometry

Year: 2025

Type: article

Abstract: Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. In the slab geometry, the motion takes place between two infinite membranes. Like in previous investigations, the asymptotic regime of high tumbling rates is of particular interest. This work provides local existence and uniqueness of solutions to the kinetic equation and shows their convergence towards solutions of a parabolic Keller–Segel model in the asymptotic limit. In addition, convergence rates with respect to the asymptotic parameter are established under additional regularity assumptions on the problem data. Particular difficulties in the analysis are caused by vanishing velocities in the kinetic model as well as the occurrence of boundary terms.

Source: Asymptotic Analysis

DOI: 10.1177/09217134251328514

Authors: Herbert Egger, Kathrin Hellmuth, Nora Philippi, Matthias Schlottbom

Institutions: Johannes Kepler University of Linz, Johann Radon Institute for Computational and Applied Mathematics, University of Würzburg, University of Twente

Language: English

Topic: Mathematical Biology Tumor Growth

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,150

Funders: Deutsche Forschungsgemeinschaft, Studienstiftung des Deutschen Volkes