Physiologically structured populations with diffusion and dynamicboundary conditions - József Z. Farkas; Peter Hinow (Mathematical Biosciences and Engineering)
We consider a linear size-structured population model with diffusion in thesize-space. Individuals are recruited into the population at arbitrary sizes.We equip the model with generalized Wentzell-Robin (or dynamic) boundaryconditions. This approach allows the modelling of populations in whichindividuals may have distinguished physiological states. We establishexistence and positivity of solutions by showing that solutions are governed bya positive quasicontractive semigroup of linear operators on thebiologically relevant state space. These results are obtained by establishingdissipativity of a suitably perturbed semigroup generator. We also show thatsolutions of the model exhibit balanced exponential growth, that is, our modeladmits a finite-dimensional global attractor. In case of strictly positivefertility we are able to establish that solutions in fact exhibit asynchronousexponential growth.