Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 69-105 |
| Seitenumfang | 37 |
| Fachzeitschrift | Journal of Elliptic and Parabolic Equations |
| Jahrgang | 4 |
| Ausgabenummer | 1 |
| Frühes Online-Datum | 7 Feb. 2018 |
| Publikationsstatus | Veröffentlicht - 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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
- Mathematik (insg.)
- Numerische Mathematik
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in: Journal of Elliptic and Parabolic Equations, Jahrgang 4, Nr. 1, 04.2018, S. 69-105.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -