Nonlocal diffusion elliptic system modelling the behaviour of a bacteria and a living nutrient
Marcos Antonio Viana Costa, Yino B. Cueva Carranza, Cristian Morales-Rodrigo, António Suárez · Discrete and Continuous Dynamical Systems - B · 2024
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.