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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.


- 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.   Morales-Ruiz (Technical Univ. of Madrid)

- Jean-Michel Roquejoffre (Université Paul Sabatier, Toulouse)
  • Supported by FME, UPC


- 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
- Jean-Michel 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).


NEWS: Bank account to pay conference registration JISD2015

*2100 0655 78 0200369725*. / *IBAN: ES52 2100 0655 7802 0036 9725* / *SWIFT: CAIXESBBXXX*

with the subject "Payment registration fee JISD'15_firstname_lastname"

Please, when you made the transfer,send a copy of payment (pdf by e-mail)
your name to rosa.maria.cuevas@upc.edu.


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.

Stochastic homogenization, regularity and optimal quantitative estimates

Scott Armstrong (Université Paris 9)

In this mini-course 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.
Reaction-diffusion and propagation in non-homogenous media

Henri Berestycki (EHESS, Paris)


The classical theory of reaction-diffusion 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 reaction-diffusion 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 non-linear parabolic and elliptic equations. It is also of interest to consider cases with non-local 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 non-local operators, (iv) principal eigenvalues of elliptic operators in unbounded domains, (v) propagation and spreading speeds in non-homogeneous media, (vi) the effect of the geometry of the domain on propagation or blocking of waves.

Non-equilibrium steady states

Jean Pierre Eckman (Université de Genève)

I plan to discuss the theory of non-equilibrium 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 hypo-ellipticity: 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, Navier-Stokes, and other Geophysical Models

Edriss S. Titi (Weizmann Institute and Texas A&M University)

Prof. Titi's slides (PDF1, PDF2, PDF3)

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 Navier-Stokes 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 Navier-Stokes equations.
Seminars Abstract

Juan  J.   Morales-Ruiz (Technical Univ. of Madrid)


Solitons and Differential Galois Theory

This talk will be devoted to an application of  the Differential Galois Theory to  theso-called "pde's integrable  evolution equations", ie,equations with "solitonic" solutions, like KdV  (Korteweg de Vries), Sine-Gordon, 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 like-solitons 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 Sánchez-Cauce  and  Maria-Ángeles Zurro.
Jean-Michel Roquejoffre (Université Paul Sabatier, Toulouse).

Uniqueness in a class of Hamilton-Jacobi equations with constraints.
The model under study is a time-dependent Hamilton-Jacobi 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 selection-mutation model in poulation dynamics, which exhibits concentration on the zero level set of the solution of the Hamilton-Jacobi equation. The uniqueness result implies strong convergence and error estimates for the selection-mutation model.
Joint work with S. Mirrahimi



(*) For further details, please contact: rosa.maria.cuevas .at. upc.edu


10-06-2015 - RMC