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 flame-flow interaction with the aim of improving current
understanding of the underlying mechanisms.
patches as localized solutions of a reaction-diffusion system
communities in water limited systems can be described by
reaction-diffusion equations for the plant-biomass 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
The topic of water-limited 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
reaction-diffusions giving rise to solution with blow-up in finite
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.
–diffusion with non local termd and other effects
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 reaction-diffusion processes, will be also
terms in reaction-diffusion systems
reaction-diffusion equations (as for instance, the ones arising in
2-d space charge
electron problem or in the Thomas-Fermi 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.
mathematical models of blood coagulation will be analysed.
methods for two-phase flow in porous media.
We investigate a
newly developed variant of the finite volume method for
convection-reaction-diffusion 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.
interacting particle systems
The aim is to
construct a rigorous framework for the upscaling of interacting
particle systems to macroscopic diffusion processes.