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Comparison principles for impulsive parabolic equations with applications to models of single species growth

Published online by Cambridge University Press:  17 February 2009

L. H. Erbe ,
H. I. Freedman ,
X. Z. Liu  and
J. H. Wu
L. H. Erbe
Affiliation:
Applied Mathematics Institute, University of Alberta, Edmonton, CanadaT6G 2G1.
H. I. Freedman
Affiliation:
Applied Mathematics Institute, University of Alberta, Edmonton, CanadaT6G 2G1.
X. Z. Liu
Affiliation:
Applied Mathematics Institute, University of Alberta, Edmonton, CanadaT6G 2G1. Present address: Department of Applied Mathematics, University of Waterloo, Waterloo, Canada.
J. H. Wu
Affiliation:
Applied Mathematics Institute, University of Alberta, Edmonton, CanadaT6G 2G1. Present address: Department of Mathematics, York University, North York, Canada.
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Abstract

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This paper establishes some maximum and comparison principles relative to lower and upper solutions of nonlinear parabolic partial differential equations with impulsive effects. These principles are applied to obtain some sufficient conditions for the global asymptotic stability of a unique positive equilibrium in a reaction-diffusion equation modeling the growth of a single-species population subject to abrupt changes of certain important system parameters.

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 4 , April 1991 , pp. 382 - 400
Copyright
Copyright © Australian Mathematical Society 1991

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