Vol. 13, No. 1, 2020

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Analysis of steady states for classes of reaction-diffusion equations with hump-shaped density-dependent dispersal on the boundary

Quinn Morris, Jessica Nash and Catherine Payne

Vol. 13 (2020), No. 1, 9–19
Abstract

We study a two-point boundary-value problem describing steady states of a population dynamics model with diffusion, logistic growth, and nonlinear density-dependent dispersal on the boundary. In particular, we focus on a model in which the population exhibits hump-shaped density-dependent dispersal on the boundary, and explore its effects on existence, uniqueness and multiplicity of steady states.

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Keywords
differential equation, mathematical ecology, nonlinear dispersal, nonlinear boundary condition, logistic equation, reaction-diffusion equation, density-dependent dispersal
Mathematical Subject Classification 2010
Primary: 34B18, 34C60, 92D25
Milestones
Received: 14 May 2018
Revised: 13 June 2019
Accepted: 2 October 2019
Published: 4 February 2020

Communicated by Kenneth S. Berenhaut
Authors
Quinn Morris
Swarthmore College Swarthmore, PA
United States
Appalachian State University
Boone, NC
United States
Jessica Nash
The University of North Carolina at Greensboro
Greensboro, NC
United States
Catherine Payne
Department of Mathematics
Winston-Salem State University
Winston-Salem, NC
United States