Local travelling wave solutions and self-similar solutions for a green roof model
Abstract
In this thesis we study travelling wave solutions and self-similar solutions for
a green roof model and for some simpler models which are derived from that
model. We focus on two limiting cases near a dry region and near a saturated
region.
We start by considering a convection model in the absence of diffusion and sink
terms. We show that rarefaction waves and shock solutions exist for several
cases.
Next, we consider a convection-diffusion model where both the convective and
diffusive terms are present and we show that travelling wave solutions and
self-similar solutions exist for some cases. Moreover, numerical simulations are
used for the travelling wave and self-similar solutions and confirm the analytic
predictions.
Finally, we consider the green roof model where all terms are present and we
show that travelling wave solutions exist, whereas self-similar solutions are not
found. We also show the travelling wave solutions exist for the two limiting
cases.