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

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  03 April 2019

Qi Wang ,
Jingyue Yang  and
Feng Yu
Qi Wang*
Affiliation:
Department of Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan611130, China (qwang@swufe.edu.cn)
Jingyue Yang
Affiliation:
Department of Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan611130, China (yjy@2011.swufe.edu.cn)
Feng Yu
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, FL32816, USA (yfeng@knights.ucf.edu)
*
*Corresponding author.
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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.

Keywords

Lotka–Volterra competition systemnonlinear diffusionglobal existenceboundedness

MSC classification

Primary: 35K51: Initial-boundary value problems for second-order parabolic systems
Secondary: 35K55: Nonlinear parabolic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 5 , October 2020 , pp. 2322 - 2348
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Copyright
Copyright © Royal Society of Edinburgh 2019

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