Kinks and solitons in linear and nonlinear-diffusion Keller-Segel type models with logarithmic sensitivity

2021/02/26 by Juan Campos, Campos, Juan, Claudia García +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #335A15 #35A01 #35B44 #35C07 #35K57 #35K65 #35Q92 #5B40 #92C17 #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2102.13480

openalex publication_date 2021/02/26 · openalex created_date 2021/03/15 · openalex updated_date 2026/07/28

Abstract

This paper investigates the existence of traveling--wave--type patterns in the Keller--Segel model with logarithmic sensitivity. We consider both the linear diffusion case and the nonlinear, flux-saturated diffusion of relativistic heat--equation type, providing a detailed comparison between the two regimes. Particular attention is devoted to traveling waves exhibiting compact support or support restricted to a half-line. We rigorously establish the existence of such patterns and highlight the qualitative differences arising from the choice of diffusion mechanism.

Citations

• A user’s guide to PDE models for chemotaxis
• On reaction processes with saturating diffusion

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