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arXiv · 1605.05308

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

Qi Wang·Jingyue Yang·Feng Yu
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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.

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Qi Wang, Jingyue Yang, Feng Yu. 2019-05-18. Global well-posedness of advective Lotka-Volterra competition systems with nonlinear diffusion. https://doi.org/10.1017/prm.2019.10

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