Global well-posedness of advective Lotka-Volterra competition systems with nonlinear diffusion

TL;DR

This paper establishes the global existence and boundedness of solutions for nonlinear diffusion Lotka-Volterra systems with advection, showing that attraction effects can prevent blowups in these ecological models.

Contribution

It proves the global well-posedness of reaction-advection-diffusion Lotka-Volterra systems with nonlinear diffusion, including fully parabolic and parabolic-elliptic cases, under specific growth conditions.

Findings

Global solutions exist and are uniformly bounded.

Attraction (positive taxis) inhibits blowups.

Results apply to both parabolic and parabolic-elliptic systems.

Abstract

This paper investigates the global well-posedness of a class of reaction-advection-diffusion models with nonlinear diffusion and Lotka-Volterra dynamics. We prove the existence and uniform boundedness of the global-in-time solutions to the fully parabolic systems under certain growth conditions on the diffusion and sensitivity functions. Global existence and uniform boundedness of the corresponding parabolic-elliptic system are also obtained. Our results suggest that attraction (positive taxis) inhibits blowups in Lotka-Volterra competition systems.