English

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

Analysis of PDEs 2025-12-04 v2

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.

Keywords

Cite

@article{arxiv.2102.13480,
  title  = {Kinks and solitons in linear and nonlinear-diffusion Keller-Segel type models with logarithmic sensitivity},
  author = {Juan Campos and Claudia García and Carlos Pulido and Juan Soler},
  journal= {arXiv preprint arXiv:2102.13480},
  year   = {2025}
}
R2 v1 2026-06-23T23:32:41.853Z