Nonlinear Partial Differential Equations arising from Geometry and Physics

This Research School is intended for the study of Partial Differential Equations (PDEs) arising in geometry and physics. The major PDEs classes will be considered (elliptic, parabolic and hyperbolic), both for the construction of particular solutions and the classification of different qualitative behavior scenarios. Through the 6 courses, students will be given the opportunity to know the state of the art of the subject, with an introduction to the most recent techniques. The major techniques will be presented alongside with their latest developments, in particular the fixed-point method, variational and energy methods, spectral analysis and linearization. Furthermore, the links between PDEs and geometry will be explored, with some focus on geometrical flows. Finally, we will present some applications of PDEs, for example in fluid mechanics.

This school provides an opportunity to celebrate the 60th birthday of Professor Abbas BAHRI. The MIMS (Mediterrannean Institute of Mathematical Sciences www.mims.tn) is the main organizer of this school.