WPB1. Mathematical
modelling of some open problems in flame propagation 
The objective of
the proposed research is the development and exploration of new
mathematical models for a selection of combustion phenomena related
to flameflow interaction with the aim of improving current
understanding of the underlying mechanisms. 
WPB2.
Plant community
patches as localized solutions of a reactiondiffusion system 
Plant
communities in water limited systems can be described by
reactiondiffusion equations for the plantbiomass and water
variables. Numerical integration of the equations reveals stationary
pulse solutions. These solutions provide important information about
species assemblage properties such as species richness, abundance
and composition.
The topic of waterlimited ecosystems is of extreme importance in
many countries and especially in Spain (because of the
desertification process in southern
Spain: a World
Coordination Center for the study of desertification is established
in Almeria). 
WPB3.
Higher order
reactiondiffusions giving rise to solution with blowup in finite
time. 
In contrast with
second order systems, the case of a diffusion given by higher order
differential equation is badly understood (many methods available
for second order systems can not be applied). Special energy,
symmetry, numerical methods and the classification of the solutions
in terms of the initial data must be obtained. 
WPB4.
Reaction
–diffusion with non local termd and other effects 
Very interesting
nonlinear problems in biology, population dynamics are depending on
nonlocal quantities (as for instance the total population for
population issues). The analysis to be done, for instance to
determine the asymptotic behaviour in time of such problems, is non
trivial since the usual techniques of reaction diffusion systems or
equations fail. Also the stationary points associated to these
problems can be very numerous which complicates the behaviour of
such systems. Problems set in cylinders or depending on periodic
data are expected to present some interesting properties when the
size of the domain where they are set is growing. Other effects,
arising in some reactiondiffusion processes, will be also
considered. 
WPB5:
Singular
terms in reactiondiffusion systems 
Many
reactiondiffusion equations (as for instance, the ones arising in
2d space charge
electron problem or in the ThomasFermi equation) lead to the
presence of no differentiable or singular reaction terms. The study
of the interface generated by the solutions will be the main
difficulty in this study.
Some special
mathematical models of blood coagulation will be analysed.

WPB6.
Finite volume
methods for twophase flow in porous media. 
We investigate a
newly developed variant of the finite volume method for
convectionreactiondiffusion systems. This will permit to include
inhomogeneous and anisotropic diffusion terms and to write efficient
programs in the case of real geological meshes as is of interest for
the Guigues Environment. We shall also extend our research to the
simulation of multiphase flow in porous media. 
WPB7.
Upscaling of
interacting particle systems 
The aim is to
construct a rigorous framework for the upscaling of interacting
particle systems to macroscopic diffusion processes.
