Article Contents

2025, Volume 30, Issue 1: 82-98. Doi: 10.3934/dcdsb.2024080

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Nonlocal diffusion elliptic system modelling the behaviour of a bacteria and a living nutrient

1.
Dpto. de Matemática e Computação, Universidade Estadual Paulista (UNESP), Faculdade de Ciências e Tecnologia, Presidente Prudente, Brasil
2.
Dpto. de Ecuaciones Diferenciales y Análisis Numérico and IMUS, Facultad de Matemáticas, Universidad de Sevilla, Sevilla, España

^*Corresponding author: Antonio Suárez
^*Corresponding author: Antonio Suárez

Received: January 2024

Revised: May 2024

Early access: June 2024

Published: January 2025

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Abstract

In this paper, we discuss the existence and uniqueness of coexistence states for a class of non-local elliptic system. This problem models the behaviour of a bacteria and a living nutrient, whose diffusion depends on the population of the bacteria in a non-local and nonlinear way. Mainly, we employ bifurcation methods and the Implicit Function Theorem to obtain the existence and uniqueness of positive solution.

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Mathematics Subject Classification: Primary: 35B09, 35B32, 35J47, 92B05.

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References

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