# Nonlinear PDE`s @ IMPA – 2016

IMPA, Rio de Janeiro, June 20 – 24, 2016

The field of nonlinear partial differential equations has experienced a striking evolution over the last fifteen years in Brazil. The number of PhD’s and students has increased creating a critical mass. In this process it is fundamental to have a scientific interchange with researchers leaders in the field. The aim of the workshop is to continuing this process by allowing the community to attend to lectures of recent and important progress in the field delivered by renowned specialists. The workshop will bring together leading experts in nonlinear dispersive equations, nonlinear hyperbolic systems of conservation laws, nonlinear elliptic equations and free-boundary problems. Graduate students and young PhD’s are encouraged to participate of this meeting.

## Group Picture

## Certificates

## Videos of the Talks

## Registration

**Registration fee**

Category |
Price |

Researchers and Professors (Ph.D’s) |
R$ 200.00 |

Students (Master and Ph.D) |
R$ 80.00 |

IMPA´s Students |
R$ 50.00 |

## Organizing and Scientific Committee

## Conference Topics

**The main themes in the workshop Nonlinear PDE’s @ IMPA will be:**

– Nonlinear Dispersive Equations.

– Nonlinear Hyperbolic systems of Conservation Laws.

– Nonlinear Elliptic Equations.

– Free-Boundary Problems

**The meeting will also include related topics such as:**

– Equations of Fluid Mechanics.

– Kinetic Equations.

– Optimal Transport

– Variational Problems.

– Homogenization.

## Program

## Plenary Speakers

Luis Caffarelli (University of Texas at Austin, USA)

Some non local versions of the Monge Ampere equation

Thierry Cazenave (Univ. Paris 6, France)

Regularity issues in semilinear Schrödinger and heat equations

Vladimir Georgiev (University of Pisa)

Scattering of small solutions of the cubic NLS with short range potential

Kenneth H. Karlsen (University of Oslo)

Stochastic Conservation Laws

Yanyan Li (Rutgers University)

Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations

Ronghua Pan (Georgia Tech)

Global regularity v.s. finite time blowup for compressible Euler equations

Jean-Claude Saut (Univ. Paris Sud, France )

Full dispersion water waves models

Denis Serre (Ecole Normale Superieure Lyon, France)

The singularity of a perfect gas at the vacuum boundary

## 30-Minute Talks

Ricardo Alonso (PUC)

Short introduction to one dimensional dissipative Boltzmann equation

Miguel Angel Alejo (Universidade Federal de Santa Catarina)

Stability of Breathers and Numerical Results

Jaime Angulo (USP)

Stability of Peak Solutions for Nls Equations with Point Interactions

Stefan Berres (Universidad Católica de Temuco, Chile)

Identification of shock profile solutions for bidisperse suspensions

Raimund Bürger (Universidad de Concepción, Chile)

A random sampling approach for a family of Templeclass systems of conservation laws

Emanuel Carneiro (IMPA)

On the regularity of maximal operators on BV spaces

Marcelo M. Cavalcanti (State University of Maringá)

Unilateral Problem for the Wave Equation With Spatial-Time Degenerate Nonlinear Damping: Well-Posedness And Exponential Stability

Gyula Csato (Universidad de Concepción, Chile)

About the Hardy-Sobolev, Moser-Trudinger and isoperimetric inequalities with densities

German Fonseca (Universidad Nacional, Bogota)

Generalized Zakharov-Kuznetsov equation in anisotropic weighted Sobolev spaces

Olivier Kneuss (Universidade Federal do Rio de Janeiro)

Nelson’s conjecture revisited

Yachun Li (Shanghai Jiao Tong University, China)

Global Classical Solutions to the Cauchy Problem of Conservation Laws with Degenerate Diffusion

Diego Moreira (UFC)

Hopf-Oleinik Lemma and Applications

Claudio Muñoz (Universidad de Chile)

Well-posedness for the Novikov-Veselov equation

Wladimir Neves (UFRJ)

Stochastic transport equation in bounded domains

Ademir Pastor (UNICAMP)

Scattering for a 3D Coupled Nonlinear Schrodinger System

Ademir Fernando Pazoto (UFRJ)

Stabilization of a Boussinesq system with generalized damping

Didier Pilod (UFRJ)

Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation

Edgard Pimentel (UFSCar)

A priori Sobolev regularity for fully nonlinear parabolic equations

Moritz Reintjes (IMPA)

Is Spacetime Locally Inertial for General Relativistic Shock Wave Solutions?

Jean Carlos da Silva (UFRJ)

On The Almost Periodic Homogenization of Non-Linear Scalar Conservations Laws

Boyan Sirakov (PUC)

A Priori Bounds for Elliptic Inequalities via Regularity Estimates

Erlend Briseid Storrosten (University of Oslo)

Error Estimates for Finite Difference Approximations of Degenerate Convection-Diffusion Equations

## Short Communications

Eduardo Arbieto Alarcon (Universidade Federal de Goiás)

On the Cauchy Problem Associated to the Brinkman Flow in R^{n}_{+}

Pablo Braz e Silva (Universidade Federal de Pernambuco)

Some asymptotic supnorm estimates for convection-diffusion equations and systems

Gerardo Camacho-de La Rosa (University of Mexico)

Existence and Stability of the Travellingwave Solutions for a Semilinear Wave Equation

Roberto Capistrano-Filho (Universidade Federal de Pernambuco)

Neumann Boundary Controllability of the Korteweg-De Vries Equation

Hernán Castro (Universidad de Talca)

Hardy-Sobolev Type Inequalties with Monomial Weights

Márcio Cavalcante de Melo (Universidade Federal de Alagoas)

The Initial-Boundary-Value Problem For Some Quadratic Nonlinear Schrodinger Equations On The Half-Line

Liliana Esquivel (UNAM Campus Morelia)

Neumann problem for nonlinear Schrödinger equation with the Riesz fractional derivative operator

Marco A. M. Guaraco (IMPA)

Geometric min-max methods and the space of solutions to the Allen-Cahn equation on closed manifolds

Isnaldo Isaac Barbosa (Universidade Federal de Alagoas)

On the Cauchy Problem for Nonlinear Interactions type Schrödinger

Uriel Kaufmann (Universidad Nacional de Cordoba)

Positive Solutions for Singular Problems Involving the P-Laplacian

Gustavo F. Madeira (Universidade Federal de São Carlos)

Bifurcation and Stability of Steady States of Parabolic Problems Under Logistic Flux Boundary Conditions

Wanderley Nunes do Nascimento (IMEEC – UNICAMP)

Semi-linear wave models with power non-linearity and scale-invariant time-dependent mass and dissipation

Tiago Picon (FFCLRP/USP)

Global existence of small data solutions to the semilinear fractional wave equation

Juliana Pimentel (Universidade Federal do ABC)

Infinite time blow-up for the Chafee-Infante equation

Marcelo Rempel Ebert (Universidade de São Paulo)

Some optimal decay estimates for damped semilinear evolution equations

## Poster Session

Amanda A. Feltrin Nunes (Universidade Federal de São Carlos)

Multiple Positive Solutions for a Non-Local Quasilinear Problem from Population Genetics

Marcelo Fernandes de Almeida (Federal University of Sergipe)

Uniform Global Well-Posedness of the Navier-Stokes-Corioles in a new Critical Space

Fernando A. Gallego (Universidade Federal do Rio de Janeiro)

Neumann Boundary Controllability of the Gear-Grimshaw System with Critical Size Restrictions on the Spacial Domain

Carlos M. Guzmán (Universidade Federal de Minas Gerais)

On the inhomogeneous nonlinear Schrödinger equation

Alex Hernandez Ardila (IME-USP)

Stability of ground states for logarithmic Schrödinger equation with a δ‘-interaction

Lucas Fabiano Lima (Universidade Federal de São Carlos)

Regularity Theory for a Mean-Field Game Model of Wealth and Capital Accumulation

Cecilia Saavedra Fresia (Universidad Nacional de Tucumán)

EDP’s no Lineales en el Sistema Vascular

César K. Soares dos Santos

Pointwise regularity for a parabolic equation with log-term singularity

## Call For Abstracts

Besides the main lectures, there will be 30 minutes lectures, 20 minutes short communications and posters. We would like to invite the interested to submit abstracts for these presentations. The abstract should be no longer than 2 pages in PDF or PS format. Full consideration will be given to abstracts which are submitted before April 15th, 2016. The accepted presentations will be communicated by April 30th, 2016.

Be sure your abstract includes the title, and all author names and addresses, indicating who is going to present.

It is strongly recommended that the following template be used to produce the pdf file:

Please click here to download the template.

Please send the abstract by e-mail to: nlpde@impa.br

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## List of Registered Participants

**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