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Asymptotic profiles for positive solutions of diffusive logistic equations

Part of: Parabolic equations and systems Partial differential equations

Published online by Cambridge University Press:  15 February 2023

Jian-Wen Sun  and
Peng-Fei Fang
Jian-Wen Sun
Affiliation:
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China (jianwensun@lzu.edu.cn)
Peng-Fei Fang
Affiliation:
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China (jianwensun@lzu.edu.cn)
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Abstract

In this paper, we study the asymptotic profiles of positive solutions for diffusive logistic equations. The aim is to study the sharp effect of linear growth and nonlinear function. Both the classical reaction-diffusion equation and nonlocal dispersal equation are investigated. Our main results reveal that the linear and nonlinear parts of reaction term play quite different roles in the study of positive solutions.

Keywords

Reaction-diffusion equationpositive solutionlogistic

MSC classification

Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35K57: Reaction-diffusion equations 92D25: Population dynamics (general)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 1 , February 2024 , pp. 273 - 284
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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