Global existence and spatiotemporal pattern formation of a nutrient-microorganism model with nutrient-taxis in the sediment

In this paper, we consider a nutrient-microorganism system with nutrient-taxis in the sediment. The global existence and uniform-in-time bound of classical solutions in a domain with any dimension is established, and the linearized stability of the constant interior steady state is analyzed, which shows that different types of nutrient-taxis may (de-)stabilize the positive constant equilibrium. Moreover, over 1D domain, we obtain the local existence and stability of nonconstant steady states near the positive constant equilibrium via bifurcation theory. Finally, several numerical simulations on one- and two-dimensional spatial domains are presented, which demonstrate that this reaction-advection-diffusion system can admit numerous interesting spatio-temporal patterns.

Automated summary

This paper investigates a nutrient-microorganism system with nutrient-taxis in the sediment. The study establishes the global existence and uniform-in-time bound of classical solutions in a domain with any dimension. It also analyzes the linearized stability of the constant interior steady state, showing that different types of nutrient-taxis can (de-)stabilize the positive constant equilibrium. Additionally, the local existence and stability of nonconstant steady states near the positive constant equilibrium are obtained over a 1D domain using bifurcation theory. Several numerical simulations on one- and two-dimensional spatial domains are presented to demonstrate the system's ability to exhibit various interesting spatio-temporal patterns.