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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Physiologically Structured Populations with Diffusion and Dynamic Boundary Conditions
Author(s): Farkas, Jozsef Zoltan
Hinow, Peter
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Keywords: Structured populations
Wentzell-Robin boundary condition
Semigroups of linear operators
spectral methods
Population dynamics
Issue Date: Apr-2011
Citation: Farkas JZ & Hinow P (2011) Physiologically Structured Populations with Diffusion and Dynamic Boundary Conditions. Mathematical Biosciences and Engineering, 8 (2), pp. 503-513.;
Abstract: We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. We equip the model with generalized Wentzell-Robin (or dynamic) boundary conditions. This approach allows the modelling of populations in which individuals may have distinguished physiological states. 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. These results are obtained by 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.
DOI Link: 10.3934/mbe.2011.8.503
Rights: Published in Mathematical Biosciences and Engineering (MBE) by American Institute of Mathematical Sciences (AIMS).

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