Objectives of the programme

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A.    Mathematical models for combustion

B.    Singularities in superconductivity, liquid crystals, and micromagnetism

C.    Front propagation in biological and chemical systems

D.    Coating flows and thin liquid films

E.    Interfaces in phase transitions

F.    Blow-up problems

G.    PDE's with singular data

T.    Training of young researchers

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Mathematical models for combustion
Involves teams
Italy, The Netherlands, Israel, Spain, United Kingdom, France
with the following major goals:

• understanding of flashback and triple flames for curved flame fronts;
• solution of well-known but difficult open problems concerning laminar radiation combustion with simple chemistry;
• in the case of turbulent radiation combustion with complex chemistry, the
• adaptation of an existing industrial numerical code to the radiative case.

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Singularities in superconductivity, liquid crystals, and micromagnetism
Involves teams
Italy, The Netherlands, Germany, Israel, Greece, Spain, United Kingdom, France
with the following major goals:

• the construction of vortex ring solutions for the Gross-Pitaevskii equation;
• a rigorous derivation of the equations forvortex lines in superconductors in the presence of an external field;
• understanding of the evolution of point singularities for the heat flow of harmonic maps and its relation with nonuniqueness phenomena and spatial energy concentration.

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Front propagation in biological and chemical systems Inolves all teams,
with the following major goals:

• existence of standing and travelling waves in homogeneous and heterogeneous media;
• understanding of blocking and extinction phenomena for such waves;
• extensions of the notion of travelling front to more general geometries and equations (beyond the periodic case);
• the influence of the geometry on the speed of propagation of fronts;
• stability and instability properties of sharp fronts;
• formal limits to sharp-interface models in cases where the singular limit equations are not known and are difficult to guess.

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Coating flows and thin liquid films
Involves teams
Italy, The Netherlands, Germany, Spain, United Kingdom,
with the following major goals:

• incorporation of a range of new physical effects into existing models, such as non-isothermal or non-newtonian effects, and effects due to the presence of surfactants or phase change or non-uniform and deformable substrates;
• the development of new mathematical tools to study effectively the new models.

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Interfaces in phase transitions Involves all teams,
with the following major goals:

• global existence results of solutions of parabolic systems with applications to the inhomogeneous Allen-Cahn equation, the Mullins-Sekerka problem, mean-curvature flow and the Stefan problem with the Gibbs-Thomson law;
• new regularity results for sharp interfaces;
• better insight in sharp-interface properties from numerical simulations

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Blow-up problems
Involves teams
Italy, The Netherlands, Slovakia, Israel, Greece, Spain, United Kingdom, France
with the following major goals:

• new results on blow-up profiles;
• the continuation of solutions beyond the singularity

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PDE's with singular data
Involves teams
Italy, The Netherlands, Slovakia, Israel, Greece, Spain, France
with the following major goals:

• development of a unified method for characterizing the Radon measures which appear as a boundary trace of a positive solution;
• extension of existing results to the case of non-smooth domains or variable absorption term which may vanish at the boundary;
• understanding of the trace of solutions with changing sign and the links to certain spaces of distributions.

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Training of young researchers