Physiologically structured populations with diffusion and dynamic boundary conditions
Abstract
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary conditions. This allows modelling of "adhesion" at extremely small or large sizes. We establish existence and positivity of solutions by showing that solutions are governed by a positive quasicontractive semigroup of linear operators on the biologically relevant state space. This is carried out via establishing dissipativity of a suitably perturbed semigroup generator. We also show that solutions of the model exhibit balanced exponential growth, that is our model admits a finite dimensional global attractor. In case of strictly positive fertility we are able to establish that solutions in fact exhibit asynchronous exponential growth.
Cite
@article{arxiv.1004.4141,
title = {Physiologically structured populations with diffusion and dynamic boundary conditions},
author = {J. Z. Farkas and P. Hinow},
journal= {arXiv preprint arXiv:1004.4141},
year = {2019}
}