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Eleventh
WORKSHOP ON INTERACTIONS BETWEEN DYNAMICAL SYSTEMS AND
PARTIAL DIFFERENTIAL EQUATIONS (JISD2013)

JORNADES D'INTERACCIÓ ENTRE SISTEMES DINÀMICS I EQUACIONS EN DERIVADES PARCIALS


Barcelona, July 15 - 19, 2013

 

VENUE - Contents - Schedule - Seminars, Communications and Posters

 

The eleventh edition of the WORKSHOP ON INTERACTIONS BETWEEN DYNAMICAL SYSTEMS AND PARTIAL DIFFERENTIAL EQUATIONS (JISD2013) will be held in Barcelona, July 15 - 19, 2013, at the Universitat Politècnica de Catalunya (UPC)

 

Lecturers of courses in former JISD editions

JISD Former Editions: 2002 - 2003 - 2004 - 2005 - 2006 - 2007 - 2008 - 2010 - 2011 - 2012

There will be four main courses of six hours each, some seminars, communications, and posters. The courses will be taught within the Master of Science in Advanced Mathematics and Mathematical Engineering (MAMME) of the UPC Graduate School.

Courses taught by:
- Jacques Féjoz (Université Paris-Dauphine)
- Enrique Pujals (IMPA, Rio de Janeiro)
- Sandro Salsa (Politecnico di Milano)
- Luis Silvestre (University of Chicago)

 

Supported by the FME, UPC, SCM, RSME, SEMA.


Organizers
- Xavier Cabré
- Amadeu Delshams
- Maria del Mar González
- Tere M. Seara

Scientific Committee
- Massimiliano Berti (Univ. Federico II)
- Rafael de la Llave (Georgia Tech)
- Jean-Michel Roquejoffre (Univ. Paul Sabatier. Toulouse)
- Alfonso Sorrentino (Univ. of Cambridge)
- Marco Antonio Teixeira (Univ. Estatal de Campinas)
- Juan Luis Vázquez (Univ. Autónoma de Madrid)

There will be some *financial support* available for this edition.
Deadline to apply for financial support: April 30, 2013.
Deadline to register: May 30, 2013.

 

Contents

Courses will be held in the room S02 of the FME building (Facultat de Matemàtiques i Estadística), at C/ Pau Gargallo, n. 5 Barcelona, 08028.

Course
Abstract
The search for invariant tori in Hamiltonian systems and
applications to celestial mechanics


Jaques Féjoz (Université Paris-Dauphine)

This will be a crash course in KAM theory. This theory was initiated by Kolmogorov, Arnold and Moser in the 1950's, to study the persistence of quasiperiodic motions in Hamiltonian dynamical systems. Quasiperiodic solutions lie on invariant tori, in the phase space, which are solutions of the associated Hamilton-Jacobi equation. So, we will emphasize the relation between the viewpoints of PDEs and dynamical systems, and will mention applications to the question of the stability of the solar system.
Robustly transitive dynamics

Enrique Pujals (IMPA, Rio de Janeiro)

In this course we will deal with hyperbolic systems and robustly transitive dynamics. We will deal with robust transitive partially hyperbolic systems but also with robust transitive systems which are not partially hyperbolic. We will classify partially hyperbolic systems and devote special attention to the Hamiltonian context.
Regularity of the free boundary in problems with distributed sources

Sandro Salsa (Politecnico di Milano)
Prof. Salsa's notes (PDF)
We describe new results on one and two phases problems, governed by inhomogeneous uniformly second order elliptic equations. The main focus will be on the implications "flatness implies regularity". Prerequisites: The course does not need any particularly sophisticated notion. Only: a) Basic theory for uniformly second order elliptic equations (Harnack inequality, maximum principles, Shauder estimates). b) Basic notions on solutions in the viscosity sense.
Regularity results for nonlocal equations

Luis Silvestre (University of Chicago)
Prof. Silvestre's notes (link)
We will develop some regularity results for integro-differential equations. The equations that we study come from the study of Levy processes and stochastic games related to them. We will prove some a priori estimates for the integro-differential Bellman and Isaacs equations which are generalizations of regularity results for fully non linear elliptic PDE.

(*) For further details, please contact:

xavier.cabreupc.edu, amadeu.delshamsupc.edu, mar.gonzalezupc.edu, or tere.m-searaupc.edu



06-11-2014 - Rosa Maria Cuevas

darrera modificació: Novembre 2014
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