These courses are supported by the grant Ayuda de movilidad asociada a los Masters
There will be some *financial support* available for this edition. Deadline to apply for financial support: April 30, 2010 (see Registration).
You can see the courses' schedule here
Courses will be held in the room 001 of the FME building (Facultat de Matemàtiques i Estadística), at C/ Pau Gargallo, n. 5 Barcelona, 08028.
Partial differential equations with fractional diffusion
Jean-Michel Roquejoffre (Univ. Paul Sabatier. Toulouse III)
The modelling of long distance effects in transport phenomena
sometimes involves fractional diffusion operators. The goal of this
course is to discuss various nonlinear PDE's involving the fractional
laplacian, or more general operators, and study their qualitative
properties. Sometimes the results are close to those obtained for standard
diffusion models. In other situations, notable differences occur.
Mathematical modelling of phase transitions
Tim Myers (CRM, Bellaterra, Barcelona)
The theory of phase transition is well established, following Stefans pioneering work on mod-
elling the freezing of sea ice in the 1890s. Phase change (or Stefan) problems are a specific
form of moving boundary problem with a rich mathematical theory and numerous practical
applications (e.g. melting and thawing, solidification of steel and chemical reactions). This
course will deal with the modelling, theory and applications of Stefan problems.
New connections between dynamical systems and Hamiltonian PDEs
Massimiliano Berti (Univ. Federico II)
Many partial differential equations arising in physics can be seen as infinite dimensional Hamiltonian systems. Main examples are the nonlinear wave and Schrödinger equations, the beam, the membrane and the Kirkhoff equations in elasticity theory, the Euler equations of hydrodynamics as well as their approximate models like the KdV, the Benijamin-Ono, the Boussinesq, the K-P equations, etc....
Action-minimizing methods in Lagrangian dynamics
Alfonso Sorrentino (Univ. of Cambridge)
In this course we shall present Mather and Mañé's variational
approaches to the study of convex Lagrangian (and Hamiltonian)
systems, and discuss their connection with more classical results
from KAM theory, Hamilton-Jacobi equation, symplectic geometry, etc...
For further details, please contact Xavier.Cabréupc.edu, Amadeu.Delshamsupc.edu, Mar.Gonzalezupc.edu, or Tere.M-Searaupc.edu
July, 07-2010 - RMC