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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
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Abstract |
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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. |
Keywords
differential equation, mathematical ecology, nonlinear
dispersal, nonlinear boundary condition, logistic equation,
reaction-diffusion equation, density-dependent dispersal
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Mathematical Subject Classification 2010
Primary: 34B18, 34C60, 92D25
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Milestones
Received: 14 May 2018
Revised: 13 June 2019
Accepted: 2 October 2019
Published: 4 February 2020
Communicated by Kenneth S. Berenhaut
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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 |
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| Catherine Payne | |
| Department of Mathematics Winston-Salem State University Winston-Salem, NC United States |
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