TY - JOUR
T1 - On first-order hyperbolic partial differential equations with two internal variables modeling population dynamics of two physiological structures
AU - Kang, Hao
AU - Huo, Xi
AU - Ruan, Shigui
N1 - Funding Information:
Research was partially supported by National Science Foundation (DMS-1853622).
Publisher Copyright:
© 2020, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/4
Y1 - 2021/4
N2 - In this paper we develop fundamental theories for a scalar first-order hyperbolic partial differential equation with two internal variables which models single-species population dynamics with two physiological structures such as age–age, age–maturation, age–size, and age–stage. Classical techniques of treating structured models with a single internal variable are generalized to study the double physiologically structured model. First, the semigroup is defined based on the solutions and its infinitesimal generator is determined. Then, the compactness of solution trajectories is established. Finally, spectrum theory is employed to investigate stability of the zero steady state and asynchronous exponential growth of solutions is studied when the zero steady state is unstable.
AB - In this paper we develop fundamental theories for a scalar first-order hyperbolic partial differential equation with two internal variables which models single-species population dynamics with two physiological structures such as age–age, age–maturation, age–size, and age–stage. Classical techniques of treating structured models with a single internal variable are generalized to study the double physiologically structured model. First, the semigroup is defined based on the solutions and its infinitesimal generator is determined. Then, the compactness of solution trajectories is established. Finally, spectrum theory is employed to investigate stability of the zero steady state and asynchronous exponential growth of solutions is studied when the zero steady state is unstable.
KW - Asynchronous exponential growth
KW - Infinitesimal generator
KW - Physiological structure
KW - Semigroup theory
KW - Spectrum theory
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U2 - 10.1007/s10231-020-01001-5
DO - 10.1007/s10231-020-01001-5
M3 - Article
AN - SCOPUS:85086652299
VL - 200
SP - 403
EP - 452
JO - Annali di Matematica Pura ed Applicata
JF - Annali di Matematica Pura ed Applicata
SN - 0373-3114
IS - 2
ER -