Positive Equilibrium Solutions for Age- and Spatially-Structured Population Models

The existence of positive equilibrium solutions to age-dependent population equations with nonlinear diffusion is studied in an abstract setting. By introducing a bifurcation parameter measuring the intensity of the fertility, it is shown that a branch of (positive) equilibria bifurcates from the tr...

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Published inSIAM journal on mathematical analysis Vol. 41; no. 4; pp. 1366 - 1387
Main Author Walker, Christoph
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2009
Subjects
Age
Bifurcations
Diffusion
Eigenvalues
Equilibrium
Fertility
Mathematical analysis
Mathematical functions
Mathematical models
Nonlinearity
Population
Values
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Abstract The existence of positive equilibrium solutions to age-dependent population equations with nonlinear diffusion is studied in an abstract setting. By introducing a bifurcation parameter measuring the intensity of the fertility, it is shown that a branch of (positive) equilibria bifurcates from the trivial equilibrium. In some cases the direction of bifurcation is analyzed.
AbstractList The existence of positive equilibrium solutions to age-dependent population equations with nonlinear diffusion is studied in an abstract setting. By introducing a bifurcation parameter measuring the intensity of the fertility, it is shown that a branch of (positive) equilibria bifurcates from the trivial equilibrium. In some cases the direction of bifurcation is analyzed.
Author Walker, Christoph
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Cites_doi 10.1007/BF00277394
10.1017/S095679250800733X
10.1007/BF00276556
10.1016/j.jde.2008.02.008
10.1007/BF00275825
10.1006/jmaa.1997.5554
10.2969/jmsj/1156342030
10.1016/0362-546X(83)90002-0
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10.1016/0898-1221(85)90145-2
10.3934/dcdsb.2007.7.735
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SubjectTerms Age
Bifurcations
Diffusion
Eigenvalues
Equilibrium
Fertility
Mathematical analysis
Mathematical functions
Mathematical models
Nonlinearity
Population
Values
Title Positive Equilibrium Solutions for Age- and Spatially-Structured Population Models
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