Properties of the Semigroup in $L_1$ Associated with Age-Structured Diffusive Populations
Christoph Walker
TL;DR
This paper analyzes the properties of a linear semigroup in $L_1$ related to age-structured diffusive populations, providing spectral analysis, generator characterization, and growth behavior insights.
Contribution
It offers a complete description of the semigroup's generator and spectral properties, revealing asynchronous exponential growth and regularizing effects.
Findings
Complete generator characterization in $L_1$
Spectral analysis indicating exponential growth
Regularizing effects from diffusion
Abstract
The linear semigroup associated with age-structured diffusive populations is investigated in the -setting. A complete determination of its generator is given along with detailed spectral information that imply, in particular, an asynchronous exponential growth of the semigroup. Moreover, regularizing effects inherited from the diffusion part are exploited to derive additional properties of the semigroup.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · advanced mathematical theories · Stability and Controllability of Differential Equations