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BOUNDS ON THE CRITICAL TIMES FOR THE GENERAL FISHER–KPP EQUATION

Part of: Partial differential equations Parabolic equations and systems Mathematical biology in general

Published online by Cambridge University Press:  02 November 2021

MARIANITO R. RODRIGO Open the ORCID record for MARIANITO R. RODRIGO [Opens in a new window]
MARIANITO R. RODRIGO*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales2522, Australia
*
e-mail: marianito_rodrigo@uow.edu.au
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Abstract

The Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) equation is one of the prototypical reaction–diffusion equations and is encountered in many areas, primarily in population dynamics. An important consideration for the phenomena modelled by diffusion equations is the length of the diffusive process. In this paper, three definitions of the critical time are given, and bounds are obtained by a careful construction of the upper and lower solutions. The comparison functions satisfy the nonlinear, but linearizable, partial differential equations of Fisher–KPP type. Results of the numerical simulations are displayed. Extensions to some classes of reaction–diffusion systems and an application to a spatially heterogeneous harvesting model are also presented.

Keywords

Fisher–KPP equationcritical timeupper and lower solutionspopulation dynamics

MSC classification

Primary: 35K57: Reaction-diffusion equations
Secondary: 92B05: General biology and biomathematics 35B51: Comparison principles
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 4 , October 2021 , pp. 448 - 468
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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