Global well-posedness of advective Lotka-Volterra competition systems with nonlinear diffusion
Analysis of PDEs
2019-05-21 v2
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.
Keywords
Cite
@article{arxiv.1605.05308,
title = {Global well-posedness of advective Lotka-Volterra competition systems with nonlinear diffusion},
author = {Qi Wang and Jingyue Yang and Feng Yu},
journal= {arXiv preprint arXiv:1605.05308},
year = {2019}
}