Physiologically structured populations with diffusion and dynamic boundary conditions

Details Physiologically structured populations with diffusion and dynamic boundary conditions Physiologically structured populations with diffusion and dynamic boundary conditions

2010-04-23

arxiv.org/abs/1004.4141v2

Mathematical Biosciences and Engineering, Vol.8, (2011), 503-513

Mathematics

Analysis of PDEs

Scientific paper

10.3934/mbe.2011.8.503

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.

Affiliated with

Also associated with

No associations

Rating

Physiologically structured populations with diffusion and dynamic boundary conditions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Physiologically structured populations with diffusion and dynamic boundary conditions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Physiologically structured populations with diffusion and dynamic boundary conditions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-694561