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WPB1. Mathematical modelling of some open problems in flame propagation |
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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. |
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WPB2. Plant community patches as localized solutions of a reaction-diffusion system |
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Plant 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 and composition. 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 in Almeria). |
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WPB3. Higher order reaction-diffusions giving rise to solution with blow-up in finite time. |
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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. |
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WPB4. Reaction –diffusion with non local termd and other effects |
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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 reaction-diffusion processes, will be also considered. |
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Many 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. Some special mathematical models of blood coagulation will be analysed. |
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WPB6. Finite volume methods for two-phase flow in porous media. |
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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. |
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The aim is to construct a rigorous framework for the upscaling of interacting particle systems to macroscopic diffusion processes.
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