On first-order hyperbolic partial differential equations with two internal variables modeling population dynamics of two physiological structures

Hao Kang, Xi Huo, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)403-452
Number of pages50
JournalAnnali di Matematica Pura ed Applicata
Volume200
Issue number2
DOIs
StatePublished - Apr 2021

Keywords

  • Asynchronous exponential growth
  • Infinitesimal generator
  • Physiological structure
  • Semigroup theory
  • Spectrum theory

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint

Dive into the research topics of 'On first-order hyperbolic partial differential equations with two internal variables modeling population dynamics of two physiological structures'. Together they form a unique fingerprint.

Cite this