A chemotaxis-consumption model with boundary inflow of a nutrient, steady states

Frederic Heihoff; Piotr Knosalla

A chemotaxis-consumption model with boundary inflow of a nutrient, steady states

Analysis of PDEs 2026-07-09 v1

Authors: Frederic Heihoff , Piotr Knosalla

Abstract

In this manuscript we consider the steady state problem for a chemotaxis-consumption model with positive inflow of a nutrient across the boundary. We show that in any bounded smooth domain there exists a unique nonconstant steady state provided that the mass of bacteria is sufficiently large. We further prove that, if the domain is a ball, this condition can be dropped and solutions exist for any positive bacterial mass.

Keywords

chemotaxis-consumption model boundary inflow steady states nonconstant solutions bounded smooth domain

Cite

@article{arxiv.2607.08916,
  title  = {A chemotaxis-consumption model with boundary inflow of a nutrient, steady states},
  author = {Frederic Heihoff and Piotr Knosalla},
  journal= {arXiv preprint arXiv:2607.08916},
  year   = {2026}
}

Comments

13 pages