This Programme aims at the study of global and geometric properties of solutions of nonlinear partial differential equations (PDEs), from the view point of theory and applications.
Many problems in physics, medicine, finance and industry can be described by nonlinear partial differential equations. Their investigation has, in its own turn, become an independent field with many research directions. One of these, which this proposal is based on, is the analysis of geometric and global aspects of their solutions.
Particular problems, which will be considered by this Programme, are optimal transportation problems, free boundary problems, nonlinear diffusive systems, singular perturbations, nonlinear stochastic PDEs, regularity issues and global solutions of PDEs.
All the members of the present group have years of experience in PDE-research, complemented by their other research expertises (in abstract analysis, modelling with differential equations, numerical analysis). Joining the individual scientists of this group in a coherent activity and a coordination of the European mathematicians working within the proposed subject will definitely have a strong positive impact for
• Solution of open questions,
• Formulation of new problems and opening up of new research directions,
• Stimulation of interdisciplinary contacts,
• Training of students and junior researchers.