| Speaker: | Fabien Marpeau, Texas A&M University |
| Title: | Modelization of interactions between populations and environment |
| Time: | 3:00-4:00 pm |
| Place: | Blocker 628 |
We shall be concerned with the impact of a
non-environmentally-friendly environment on populations. This talks
is split into two parts.
In the first part, we derive and analyse numerically a
reaction-diffusion system modeling the impact of a pollution on a
population set that is hierarchically organized in a food chain.
Each population is divided into two classes: the susceptible
individuals, that have never been in contact with the contamination
source, and the exposed individuals. We construct a second order
space-time numerical scheme that offers nonnegative discrete
population densities. Besides, this scheme is also relevant for
most reaction-diffusion systems arising in population dynamics, and
some diffusive transport models involving chemical reactions, as we
illustrate with several numerical tests.
In the second part, we believe that the contamination can affect
individuals at different levels, depending for example on the power
of the contamination source, and the duration of contact with the
source. In this way, the contamination is quantified and structures
the exposed individuals along a continuous scale of contamination
levels. Mathematically, the problem then consists of an
advection-reaction equation with variable speed governing the
exposed class, coupled by its boundary condition with an ordinary
differential equation, governing the susceptible class. We discuss
the existence and uniqueness of the solution to this system,
together with the uniform boundedness of the total population in
case of logistic behaviors.
Last revised: 09/24/06 By: christov@math