Nonlocal Diffusion Elliptic System Modelling The Behaviour Of a Bacteria And a Living Nutrient

2024/02/05 by Costa, M. A. V., Carranza, Y. B. C., Morales-Rodrigo, C. +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.02912

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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