Steady States of a Diffusive Population-Toxicant Model with Negative Toxicant-Taxis

• Published in: Acta applicandae mathematicae Vol. 190; no. 1; p. 13
• Main Author: Chu, Jiawei
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.04.2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Boundary conditions; Calculus of Variations and Optimal Control; Optimization; Computational Mathematics and Numerical Analysis; Heterogeneity; Mathematics; Mathematics and Statistics; Ordinary differential equations; Partial Differential Equations; Probability Theory and Stochastic Processes; Steady state; Theorems; Toxicant-taxis; Non-existence; 35J15; 35K57; Existence; 35B09; Non-constant steady states; 35Q92
• ISSN: 0167-8019; 1572-9036
• DOI: 10.1007/s10440-024-00646-1

This paper is dedicated to studying the steady state problem of a population-toxicant model with negative toxicant-taxis, subject to homogeneous Neumann boundary conditions. The model captures the phenomenon in which the population migrates away from regions with high toxicant density towards areas with lower toxicant concentration. This paper establishes sufficient conditions for the non-existence and existence of non-constant positive steady state solutions. The results indicate that in the case of a small toxicant input rate, a strong toxicant-taxis mechanism promotes population persistence and engenders spatially heterogeneous coexistence (see, Theorem  2.3 ). Moreover, when the toxicant input rate is relatively high, the results unequivocally demonstrate that the combination of a strong toxicant-taxis mechanism and a high natural growth rate of the population fosters population persistence, which is also characterized by spatial heterogeneity (see, Theorem  2.4 ).