Details
Original language | English |
---|---|
Pages (from-to) | 195-218 |
Number of pages | 24 |
Journal | Nonlinear Differential Equations and Applications |
Volume | 19 |
Issue number | 2 |
Publication status | Published - Apr 2012 |
Abstract
The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial states. The equations arise as steady state equations of an age-structured predator-prey system with spatial dispersion. Based on unilateral global bifurcation methods for Fredholm operators and on maximal regularity for parabolic equations, global bifurcation of positive solutions is derived.
Keywords
- age structure, Cross-diffusion, Fredholm operator, global bifurcation, maximal regularity
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Nonlinear Differential Equations and Applications, Vol. 19, No. 2, 04.2012, p. 195-218.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Positive solutions of some parabolic system with cross-diffusion and nonlocal initial conditions
AU - Walker, Christoph
N1 - Copyright: Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/4
Y1 - 2012/4
N2 - The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial states. The equations arise as steady state equations of an age-structured predator-prey system with spatial dispersion. Based on unilateral global bifurcation methods for Fredholm operators and on maximal regularity for parabolic equations, global bifurcation of positive solutions is derived.
AB - The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial states. The equations arise as steady state equations of an age-structured predator-prey system with spatial dispersion. Based on unilateral global bifurcation methods for Fredholm operators and on maximal regularity for parabolic equations, global bifurcation of positive solutions is derived.
KW - age structure
KW - Cross-diffusion
KW - Fredholm operator
KW - global bifurcation
KW - maximal regularity
UR - http://www.scopus.com/inward/record.url?scp=84859104063&partnerID=8YFLogxK
U2 - 10.1007/s00030-011-0124-3
DO - 10.1007/s00030-011-0124-3
M3 - Article
AN - SCOPUS:84859104063
VL - 19
SP - 195
EP - 218
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
SN - 1021-9722
IS - 2
ER -