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arXiv · 2102.13480

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

Juan Campos·Claudia García·Carlos Pulido·Juan Soler
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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.

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Juan Campos, Claudia García, Carlos Pulido, Juan Soler. 2021-02-26. Kinks and solitons in linear and nonlinear-diffusion Keller-Segel type models with logarithmic sensitivity. https://arxiv.org/abs/2102.13480

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