Details
| Original language | English |
|---|---|
| Pages (from-to) | 69-105 |
| Number of pages | 37 |
| Journal | Journal of Elliptic and Parabolic Equations |
| Volume | 4 |
| Issue number | 1 |
| Early online date | 7 Feb 2018 |
| Publication status | Published - Apr 2018 |
Abstract
We review some results on abstract linear and nonlinear population models with age and spatial structure. The results are mainly based on the assumption of maximal Lp-regularity of the spatial dispersion term. In particular, this property allows us to characterize completely the generator of the underlying linear semigroup and to give a simple proof of asynchronous exponential growth of the semigroup. Moreover, maximal regularity is also a powerful tool in order to establish the existence of nontrivial positive equilibrium solutions to nonlinear equations by fixed point arguments or bifurcation techniques. We illustrate the results with examples.
Keywords
- Age and spatial structure, Bifurcation theory, Maximal regularity, Population models
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Numerical Analysis
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In: Journal of Elliptic and Parabolic Equations, Vol. 4, No. 1, 04.2018, p. 69-105.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Some results based on maximal regularity regarding population models with age and spatial structure
AU - Walker, Christoph
PY - 2018/4
Y1 - 2018/4
N2 - We review some results on abstract linear and nonlinear population models with age and spatial structure. The results are mainly based on the assumption of maximal Lp-regularity of the spatial dispersion term. In particular, this property allows us to characterize completely the generator of the underlying linear semigroup and to give a simple proof of asynchronous exponential growth of the semigroup. Moreover, maximal regularity is also a powerful tool in order to establish the existence of nontrivial positive equilibrium solutions to nonlinear equations by fixed point arguments or bifurcation techniques. We illustrate the results with examples.
AB - We review some results on abstract linear and nonlinear population models with age and spatial structure. The results are mainly based on the assumption of maximal Lp-regularity of the spatial dispersion term. In particular, this property allows us to characterize completely the generator of the underlying linear semigroup and to give a simple proof of asynchronous exponential growth of the semigroup. Moreover, maximal regularity is also a powerful tool in order to establish the existence of nontrivial positive equilibrium solutions to nonlinear equations by fixed point arguments or bifurcation techniques. We illustrate the results with examples.
KW - Age and spatial structure
KW - Bifurcation theory
KW - Maximal regularity
KW - Population models
UR - http://www.scopus.com/inward/record.url?scp=85071248903&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1709.04445
DO - 10.48550/arXiv.1709.04445
M3 - Article
AN - SCOPUS:85071248903
VL - 4
SP - 69
EP - 105
JO - Journal of Elliptic and Parabolic Equations
JF - Journal of Elliptic and Parabolic Equations
SN - 2296-9020
IS - 1
ER -