JISD2015
13th
WORKSHOP ON INTERACTIONS BETWEEN DYNAMICAL SYSTEMS AND
PARTIAL DIFFERENTIAL EQUATIONS (JISD2015)
JORNADES D'INTERACCIÓ ENTRE SISTEMES DINÀMICS I EQUACIONS EN DERIVADES PARCIALS
Barcelona, June 1  5, 2015
 Contents  Schedule  Seminars  Communications  Posters  Participants
The 13th edition of the WORKSHOP ON INTERACTIONS BETWEEN DYNAMICAL SYSTEMS AND PARTIAL DIFFERENTIAL EQUATIONS (JISD2015) will be held in Barcelona, June 1  5, 2015, at the Universitat Politècnica de Catalunya (UPC)
Lecturers of courses in former JISD editions
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.
Lecturers:
 Scott Armstrong (Université Paris 9)
 Henri Berestycki (EHESS, Paris)
 Jean Pierre Eckman (Université de Genève)
 Edriss S. Titi (Weizmann Institute and Texas A&M Univsersity)
One hour seminars by:
 Juan J. MoralesRuiz (Technical Univ. of Madrid)
 JeanMichel Roquejoffre (Université Paul Sabatier, Toulouse)
Supported by FME, UPC
Organizers  Xavier Cabré  Amadeu Delshams  Maria del Mar González  Tere M. Seara Scientific Committee Rafael de la Llave  Alfonso Sorrentino  Luis Silvestre  Jacques Fejoz  Enrique Pujals  JeanMichel Roquejoffre  Sandro Salsa 


Registration fee: 200 euros
There will be some *financial support* available for this edition.
Deadline to apply for financial support: April 10 (results will be notified on April 20).
Deadline to register: May 15
Deadline to apply to give a communication/present a poster: April 10 (results will be notified on April 20).
REGISTRATION 13th JISD'2015 CLOSED
NEWS: Bank account to pay conference registration JISD2015
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with the subject "Payment registration fee JISD'15_firstname_lastname"
Please, when you made the transfer,send a copy of payment (pdf by email)
with your name to rosa.maria.cuevas@upc.edu.
Contents
Courses will be held in the room S04 of the FME building (Facultat de Matemàtiques i Estadística), at C/ Pau Gargallo, n. 5 Barcelona, 08028.
Course

Abstract 
Stochastic homogenization, regularity and optimal quantitative estimatesScott Armstrong (Université Paris 9)Syllabus

In this minicourse I will give a review of some recent progress in stochastic homogenization for elliptic equations, beginning with an introduction to the topic. We will consider uniformly elliptic equations exhibiting a variational structure, and energy methods will be used throughout. The focus will eventually be on proving a relation between the randomness of the coefficients and the regularity of the solutions: we will see that randomness can actually improve the smoothness of the solutions and that this regularizing effect is the key to a quantitative theory of stochastic homogenization. 
Reactiondiffusion and propagation in nonhomogenous mediaHenri Berestycki (EHESS, Paris)Syllabus

The classical theory of reactiondiffusion deals with nonlinear parabolic equations that are homogenous in space and in time. It analyses travelling waves, long time behaviour and the speed of propagation. More general, heterogeneous reactiondiffusion equations arise naturally in models of biology and medicine that lead to challenging mathematical questions. In this series of lectures, after reviewing fundamental results of the classical theory, I will describe some models that involve spatially heterogeneous nonlinear parabolic and elliptic equations. It is also of interest to consider cases with nonlocal diffusions. I will review recent progress that has been achieved with new approaches. Topics include: (i) review of classical theory, (ii) effect of lines with fast diffusion, (iii) waves guided by the medium and nonlocal operators, (iv) principal eigenvalues of elliptic operators in unbounded domains, (v) propagation and spreading speeds in nonhomogeneous media, (vi) the effect of the geometry of the domain on propagation or blocking of waves. 
Nonequilibrium steady statesJean Pierre Eckman (Université de Genève)Syllabus 
I plan to discuss the theory of nonequilibrium steady states of several systems: These studies started with the analysis of what happens when a chain of oscillators is stochastically shaken at the ends. Is there a stationary steady state? Or does the system heat up? If there is a steady state, what can one say about the energy profile along the chain? What can one say about other systems such as particles and scatterers, or chains of rotators? All these questions, and their answers (if they exist with mathematical rigor) are connected by methods of controllability and hypoellipticity: Namely, can all of phase space be reached, and does the system have a driving force which will bring it back to stationarity? After explaining the phenomenology of such systems, I will start with explaining the fundamental principles of Hoermander theory (Malliavin theory) in some toy examples, and then sketch some of the insights people have gained on this subject. 
Introductory Lectures on the Euler, NavierStokes, and other Geophysical ModelsEdriss S. Titi (Weizmann Institute and Texas A&M University)Prof. Titi's slides (PDF1, PDF2, PDF3) Syllabus

The basic problem faced in geophysical uid dynamics is that a mathematical description based only on fundamental physical principles, which are called the "Primitive Equations", is often prohibitively expensive computationally, and hard to study analytically. In these introductory lectures, aimed toward PhD students, I will survey the mathematical theory of the 2D and 3D NavierStokes and Euler equations, and stress the main obstacles in proving the global regularity for the 3D case, and the computational challenge in their direct numerical simulations. In addition, I will emphasize the issues facing the turbulence community in their turbulence closure models. However, taking advantage of certain geophysical balances and situations, such as geostrophic balance and the shallowness of the ocean and atmosphere, I will show how geophysicists derive more simplified models which are easier to study analytically. In particular, I will prove the global regularity for the 3D viscous Primitive equations of large scale oceanic and atmospheric dynamics. Moreover, I will also show that for certain class of initial data the solutions of the inviscid 2D and 3D Primitive Equations blowup in finite time. If time allows I will also discuss some new algorithms for feedback control and data assimilation for the NavierStokes equations. 
Seminars  Abstract 
Juan J. MoralesRuiz (Technical Univ. of Madrid)
Solitons and Differential Galois Theory 
This talk will be devoted to an application of the Differential Galois Theory to thesocalled "pde's integrable evolution equations", ie,equations with "solitonic" solutions, like KdV (Korteweg de Vries), SineGordon, etc. After Lax, these equations are obtained trough Lax pairs of linear differential equations. More concretely, after a minimum of necessary definitions and results on the Galois Theory of linear differential equations, the talk will be centered around the following Conjecture: the Galois group of one of the Lax pairs doesn't depends on time, i.e., the temporal evolution of the solutions must be isogaloisian. This conjecture will be verified for a classical family of rational likesolitons solutions of the KdV hierarchy obtained by Adler and Moser. Moreover we shall illustrate the above with some explicit concrete computations. The content of the talk is part of a joint work (in progress) with Sonia Jiménez, Raquel SánchezCauce and MariaÁngeles Zurro. 
JeanMichel Roquejoffre (Université Paul Sabatier, Toulouse). Uniqueness in a class of HamiltonJacobi equations with constraints. 
The model under study is a timedependent HamiltonJacobi equation, which incorporates a tuning function whose role is to keep the maximal value of the unknown at the constant value 0. The main result is that the full problem has a unique classical solution. The motivation is the singular limit of a selectionmutation model in poulation dynamics, which exhibits concentration on the zero level set of the solution of the HamiltonJacobi equation. The uniqueness result implies strong convergence and error estimates for the selectionmutation model. Joint work with S. Mirrahimi 
(*) For further details, please contact: rosa.maria.cuevas .at. upc.edu
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