# International Conference on Current Trends in Analysis and Partial Differential Equations

Thematic Program on Current Trends in Analysis and Partial Differential Equations

IMPA, Rio de Janeiro, August, 17 – 21

## Certificates

## Committees

**Organizing Committee **

Ricardo Alonso (PUC – Rio)

Emanuel Carneiro (IMPA)

Diego Moreira (UFC)

Boyan Sirakov (PUC – Rio)

Eduardo Teixeira (UFC)

**Scientific Committee**

Ricardo Alonso (PUC – Rio)

Luis Caffarelli (Texas – Austin)

Emanuel Carneiro (IMPA)

Lawrence C. Evans (Berkeley)

Irene M. Gamba (Texas – Austin)

Diego Moreira (UFC)

Boyan Sirakov (PUC – Rio)

Eduardo Teixeira (UFC)

## Invited Speakers

Ioannis Athanasopoulos – Univ. of Crete

Parabolic Obstacle Problems

Isabeau Birindelli – Univ. di Roma

Symmetry and spectral properties for viscosity solutions of fully nonlinear equations

Luis Caffarelli – Univ. of Texas – Austin

The Compresible Porous media Equation: Local and non local

Manuel Del Pino – Univ. de Chile

Infinite time bubbling in critical Parabolic equations

Laurent Desvillettes – ENS – Cachan

New results on Landau’s collision kernel for Coulomb interaction

Hermano Frid – IMPA

Global Smooth Solutions in R^{3} to Short Wave-Long Wave Interactions in Magnetohydrodynamics

Dirk Hundertmark – Karlsruhe Institute of Technology

Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules

David Jerison – MIT

Compactness and singular limits of free boundary problems in the plane

Felipe Linares – IMPA

Propagation of regularity of solutions to the k-generalized Korteweg-de Vries equation

Benoit Perthame – Université Pierre et Marie Curie – Jussieu

PDE models for neural networks; analysis and behaviour

Alexander Quaas – UTFSM – Chile

A Priori Bounds and Existence of Solutions for Some Nonlocal Elliptic Problems

Christoph Thiele – Univ. Bonn

Certain estimates on Bessel integrals and their relevance for a Fourier restriction estimate

Tatiana Toro – Univ. of Washington

Free boundary regularity for almost minimizers

José Miguel Urbano – Univ. de Coimbra

Quantitative regularity results for singular and degenerate problems

Jun-Cheng Wei – Univ. of British Columbia

On Serrin’s overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg

Noemi Wolanski – Univ. de Buenos Aires

Large time behavior for a nonlocal diffusion equation in domains with holes

Lei Zhang – Univ. of Florida

Blowup up solutions of Toda systems

## List of Registered Participants

## Contributed Talks

**Wednesday, August 19 ^{th}**

**Nome:** Wladimir Neves (UFRJ)

**Título:** Some results related to nonlocal difusion equations

**Hora:** 14:30 – 15:00

**Nome:** Damião Araújo (University of Florida)

**Título:** Geometric approach to nonvariational degenerate/singular elliptic equations

**Hora:** 15:00 – 15:30

**Nome:** Tiago H. Picon (FFCLRP-USP)

**Título:** L^{1} estimate for elliptic differential operators

**Hora:** 15:30 – 16:00

**Coffee break 16:00 – 16:30**

**Nome:** Olivaine de Queiroz (IMECC)

**Título:** Harnack type inequality versus approximation procedure in the study of a class of free boundary problems

**Hora:** 16:30 – 17:00

**Nome:** Rafayel Teymurazyan (Univ. de Coimbra)

**Título:** Optimization problems ruled by a-fractional diffusion operators with volume constrains

**Hora:** 17:00 – 17:30

**Nome:** Bertrand Lods (Universita di Torino)

**Título:** Convergence to equilibrium for subcritical solutions of the Becker–Döring equations

**Hora:** 17:30 – 18:00

## Picture of the Group

## Poster Session

__Tuesday, 18__

Francisco Albuquerque

An elliptic equation involving exponential critical growth in R^{2}

Fernando Gallego

Global well-posedness and exponential stability for the generalized KDV-burgers equation

Julio Cesar Valencia Guevara

Gradient flows of time-dependent functionals in metric spaces and applications in the Wasserstein space

Juliana Honda Lopes

A study of a non-isothermal phase- field model for two incompressible fluids

David Alexander C. Mollinedo

Uniqueness for the stochastic transport equations with bounded drift

Juliana S. Ziebell

A supnorm estimate for one-dimensional porous medium equations with advection

__Thursday, 20__

Leithold Louis Aurazo Alvarez

Global well-posedness for the Navier-Stokes equation with the coriolis force in function spaces of Besov type

Marcelo Ferreira

Multi-bump solutions for a class of quasilinear problems involving variable exponents

Márcio Cavalcante de Melo

The initial-boundary value problem for some quadratic nonlinear schrödinger equations on the half-line

Robert H. R. Guterres

Calderón-Zygmund Applications in PDEs

Thaicia Stona

The mathematics of equilibrium shapes: from geometric inequalities to the crystalline variational problem

Cilon Perusato

Leray’s Problem for the incompressible Navier-Stokes equations in R^{3}

**Instructions for Poster Presentation **

Due to the size of the poster boards your poster may not exceed 90 cm in width and 120 cm in height (portrait format). Materials for mounting the posters will be available at the poster areas.

Local organizers will provide the necessary materials for the setup, but please remember that there will be no possibility to print out the posters at the conference site.

The title and Author(s) Name(s) must appear on the top of the final poster. The poster should have a balance between the text and illustrations. The illustrations should have a bigger area of the poster. Font size should be large enough to enable reading from a certain distance. It is suggested the following font size:

Title: Size 70 (1,5cm H)

Author(s) Name(s): Size 50 (1cm H)

Text: Size 28 (0,7cm H)

**Poster Submission**

Participants, specially students, are encouraged to submit posters. For that, everybody must be registered in the School/Conference in order to submit it.

The poster proposal should include:

1. name of author

2. institution

3. title

4. Abstract (2 or 3 pages)

The text must be processed directly from LaTex to the .PDF format. The .PDF and .tex files should be sent to the e-mail eventos@impa.br no later than July 17, 2015

## Program

Program

## Registration and Financial Support – Deadline for requesting financial support: April 30th, 2015 Answer by June 5th, 2015

**Prices for Registration**

Category |
Prices |

Professors (Ph.D´s) |
R$ 120,00 |

Students (Master and Ph.D) |
R$ 60,00 |

IMPA’s Students |
R$ 40,00 |

**Postal Address: **Instituto Nacional de Matemática Pura e Aplicada

Estrada Dona Castorina 110, Jardim Botânico

Rio de Janeiro, RJ, CEP 22460-320, Brasil

E-mail: eventos@impa.br