IX Americas Conference on Differential Equations

  January 09-14, 2012,  Trujillo, Peru

Trujillo's Main Square  huanchaco

                                 Trujillo's Main Square                                                                                        Huanchaco Beach, Trujillo, Peru

The Americas Conference on Differential Equations is a biennial meeting which started in 1994, and it gathers leading experts in the areas of differential equations, dynamical systems and nonlinear analysis from the American continent, as well as special guests from Europe, to exchange ideas and results on cutting-edge research in these very active areas of science. The conference also helps initiating and enhancing ongoing research collaborations, opportunities for new collaborations, and opportunities for graduate studies and postdoctoral positions. Previous editions of this conference have been held in Mexico, Brazil, USA, Venezuela, Canada, Chile, and Colombia. The X Americas Conference is scheduled for August 2014 in Buenos Aires, Argentina. The impact of this Americas Conference is very broad, especially because new generations of young students and faculty are being recruited from all corners of the continent to join the very solid group of mathematicians formed by the top researchers who started this international event.

The IX Americas Conference on Differential Equations hosted at the Universidad Nacional de Trujillo, offered four mini-courses, and several outstanding plenary, invited and contributed talks, as well as several social activities. We had hundreds of participants from USA, Canada, Spain, France, and from several countries in Latin America; in particular, we had several faculty and students coming from Argentina, Brazil, Chile, Colombia, Mexico, Venezuela, as well as participants from 15 Peruvian universities from across the country. Everyone enjoyed Trujillo for the very warm hospitality of its people, great weather, beautiful beaches, and the spectacular Peruvian food.

Scientific Committee:                                                                    International Organizing Committee:           

Executive Committee:                                                                   Local Organizing Committee

 

For more information on the conference, including PDF files of the presentations, please visit the conference website at

https://sites.google.com/site/ixconferencia/home

 

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Some Participants at the Opening Day                                                                    Highlights of Traditional Peruvian Dances

 

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At One of the Invited Talks                                                                                Participants Visiting Chan-Chan Ruins

 

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Some of the Speakers at the Conference

 

Mini-Courses

Ekeland’s Variational Principle and Analysis in Frechet Spaces

Ivar Ekeland, University of British Columbia

Among other things, local surjection theorems and implicit function theorems in Banach spaces and Frechet spaces were presented. In contrast to the classical Nash-Moser approach, Ekeland did not use the Newton procedure, but his own Ekeland's variational principle. As a result, the function to be inverted is not required to be C2, or even C1, or even Frechet-differentiable.

 

Nonnegative Solutions of Elliptic and Parabolic Equations: Symmetry, the Nodal Structure, and Large-Time Behavior

Peter Polacik, University of Minnesota

Nonlinear elliptic and parabolic equations on symmetric domains were discussed. First, symmetry properties of nonnegative solutions were discussed. For solutions which are not strictly positive, the talk also focused on the structure of their nodal sets. It was also shown how the symmetry is used in some results on the asymptotic behavior of nonnegative solutions of parabolic equations.

 

Structural Stability and Bifurcations in the Differential Equations of Classical Geometry

Ronaldo Garcia & Jorge Sotomayor, Universidade F. de Goias,  & Universidade Sao Paulo

The topics discussed include: Generalities about  ODEs, differential  geometry, and  historical perspectives; Lines of principal curvature on surfaces immersed in Euclidean 3-D space; Lines of axial curvature on  surfaces immersed in Euclidean 4-D space; Hypersurfaces immersed in Euclidean 4-D space, and several open problems.

 

Partial Differential Equations: Control and Numerics

Enrique Zuazua, Basque Center for Applied Mathematics

Topics discussed included modeling, analysis, numerical simulation and control of PDEs arising in various contexts of science and technology. In a problem of controllability, it was analyzed whether by means of a suitable (and feasible!) controller the solution can be driven to a desired final configuration. Clasically, the dual notion of controllability is the so called observability problem. This problem is relevant for control purposes but also in other contexts like inverse problems and identification issues. There are different degrees of observability and this was particularly important in the genuinely infinite-dimensional problems considered.  A review of some of the most relevant applications to science, engineering and technology in which these problems arise was given. Then followed a discussion of the basic theory for the wave and heat equation to later address some important coupled models, as the system of thermoelasticity. These problems were also analyzed for networks of flexible strings and beams and, in particular, how the geometry of the network and the mutual lengths of the various strings/beams entering on it may influence the properties of the system in what concerns control and observation. The problem of  the numerical approximation of   control problems was also discussed. It was pointed out that when controlling a finite-dimensional approximation of  the continuous model, one does not actually compute an approximation of the control  one is looking for. The possible remedies to these pathologies are: space discretization, numerical damping, filtering of high frequencies, multi-grid algorithms,  etc.  The latter fact is of great impact form a modeling point view. Indeed, numerical approximation schemes may also be used as discrete models. The analysis showed that these two modeling approaches yield different results from a control theoretical point of view and this should be taken into account. Finally, the switching strategy, which provides a natural and efficient wat of adapting classical splitting strategies for the control of multiphysics systems was introduced.  A list of open problems and directions of possible future research was also given.

 

Plenary Talks

1. Peter Bates, Michigan State University

Persistence of Normally Hyperbolic Invariant Manifolds Under Stochastic Perturbation.

2. Alexandre Carvalho, Universidade Sao Paulo

Nonautomous Dynamics of PDEs: Gradient Evolution Processes

3. Shui-Nee Chow, Georgia Tech

Fokker-Planck Equations on a Graph with Finite Vertices.

4. Charles Doering, Universtiy of Michigan

Ultimate State of 2-D Rayleigh-Benard Convection Between Free-Slip Fixed Temperature Boundaries.

5. Duvan Henao, Pontificia Universidad Catolica de Chile

Variational Models for Cavitation in Solids.

6. John Mallet-Paret, Brown University

Dynamics of Functional Differential Equations.

7. Konstantin Mischaikow, Rutgers University

Rigorous Computation of Dynamics in Infinite Dimensions.

8. Panayotis Panayotaros, I.I.M.A.S., Universidad Nacional Autonoma de Mexico.

Nonlinear Waves in Lattices.

9. Nicolas Saintier, Universidad de Buenos Aires

Geometric Elliptic Problems.

10. Carlos Tomei, Pontificia Universidad Catolica do Rio de Janeiro

Numerical Aspects of Nonlinear Elliptic Equations with Finite Spectral Interaction.

11. Yingfei Yi, Georgia Tech

Noise Perturbation in Finite Dimension.

 

Invited Talks

  1. Antonio Capella, Universidad Nacional Autónoma de México MEXICO, A quantitative rigidity result in a model of shape memory alloys with interfacial energy.
  2. Jorge Cossio, Universidad Nacional de Colombia - COLOMBIA, Multiple solutions for a nonlinear Dirichlet problem via bifurcations.
  3. Isabel Flores, Universidad Técnica Federico Santa María de Valparaiso - CHILE,  Multiplicity of solutions for a fourth order problem with exponential nonlinearity.
  4. Luz de Teresa, Instituto de Matemáticas, Universidad Nacional Autónoma de México  MEXICO, On the controllability of hyperbolic coupled equations.
  5. Hugo Leiva, Universidad de Los Andes VENEZUELA,  Controllability of semilinear reaction diffusion equations
  6. Jorge Rebaza, Missouri State University - USA, Hopf Bifurcations and limit cycles in variable population interactions.
  7. Raul Manasevich, Universidad de Chile CHILE, Global bifurcation  for a quasilinear elliptic system of  equations modeling residential burglary.
  8. Nelson Merentes, U. Central Venezuela, Banco Central de Venezuela - VENEZUELA.   Functions of generalized bounded variation and the composition operator: from 1881 to 2011
  9. Ernesto Perez Chavela, Universidad Autónoma Metropolitana - MEXICO,Many-body problems, celestial mechanics
  10. Ramon Plaza, I.I.M.A.S.   Universidad Nacional Autónoma de México -MEXICO, Sharp Lp decay rates for perturbations of degenerate scalar viscous shocks: the return of the energy method.
  11. Gustavo Ponce, University of California Santa Barbara - USA, The IVP for the Benjamin-Ono equation in weighted Sobolev spaces
  12. Hildebrando Rodriguez-Munoz, Universidade de São Paulo - BRASIL, On a class of ODEs more general than almost periodic.
  13. Carlos Alberto Raposo de Cunha, Universidade Federal de São João del-Rei - BRASIL
  14. Noemi Wolanski, Universidad de Buenos Aires - ARGENTINA, Asymptotic behavior for a nonlocal diffusion equation in domains with holes.
  15. Maria Schonbek, University of California Santa Cruz - USA, Regularity and asymptotics of PDE's
  16. Ronaldo Alves-Garcia, Universidade Federal de Goiás - BRASIL, Darboux curves on surfaces on 3-D.
  17. Julio C. Ruiz Claeyssen, Universidad Federal do Rio Grande do Sul-BRASIL, Forced oscillations in AFM cantilevers.
  18. Jose Raul Quintero, Universidad del Valle -COLOMBIA,  Global solutions for 2-D Boussinesq-KDV type system.
  19. Pedro Isaza, Universidad Nacional de Colombia - COLOMBIA, Unique continuation principle for high order equations of KdV type
  20. Jose Arzola, Instituto Politécnico Jose Antonio Echeverria CUBA, Métodos numéricos para la consideración de la dependencia de los parámetros físicos con respecto a las variables de salida en ecuaciones diferenciales en derivadas parciales.
  21. Fabian Flores Bazan, Universidad de Concepción - CHILE Existence and strong duality for a class of non-convex variational problems.
  22. Marian Gidea, Northeastern Illinois University, Chicago, Illinois - USA,  weak stability boundary and invariant manifolds.
  23. Roxana Lopez Cruz, Universidad Nacional Mayor de San Marcos -  PERÚ,  numerical solution of a simple difussion model of influenza.

 

Contributed Talks

  1. Alexander Carrasco, Universidad Centro Occidental "Lisandro Alvarado"-UCLA - VENEZUELA  A Lemma on Evolution Operators and Applications
  2. Ambrosio Tineo, Universidad de los Andes - VENEZUELA, Regularized Evolution Operators and Applications
  3. Bladismir Leal, Universidad de los Andes - VENEZUELA, Transitivity of endomorfisms on real line
  4. Carlos Mugruza, Vasallo, University of Dundee - UK, Dynamic a causal modelling as an approach for testing cognitive networks
  5. Cesar Loza, Universidad San Luis Gonzaga- PERÚ, Teoria cuasilineal de kato
  6. Daniel Nunez, Universidad del Zulia-LUZ - VENEZUELA, On Quantifying Poincare’s Continuation Method for Nonlinear Oscillators
  7. Eddye Bustamante, Universidad Nacional de Colombia - COLOMBIA On Uniqueness Properties of Solutions of the Ostrovsky Equation with Positive Dispersion
  8. Elder Villamizar Roa, Universidad Industrial de Santander - COLOMBIA, Existence of very weak solutions for the Navier-Stokes and Boussinesq system
  9. German Lozada, Universidad Estadual Paulista - BRASIL,  On a model for invasive tumor growth.
  10. Hanzel Larez, Universidad de los Andes - VENEZUELA, Controlabilidad de algunos probelmas de frontera.
  11. Hugo Fernandez Sare, Universidade Federal do Rio de Janeiro, BRASIL, Hyperbolic Thermoelasticity: Physical approach and mathematical results
  12. Irla Mantilla, Universidad Nacional de Ingeniería - PERÚ, A finite element, level set and Uzawa methods to simulate the behavior of a fluid in a porous medium of the subsurface.
  13. Jaime Arango, Universidad del Valle de Colombia - COLOMBIA, Critical points of solutions to quasilinear elliptic problems.
  14. Jorge Avila, Universidad San Joao do Rei -  BRASIL,  Numerical Simulation of Blood Flow During the Cardiac Cycle after vascular bypass graf anastomosis.
  15. Jose Davalos Chuquipoma, Universidad San Joao do Rei -  BRASIL , Optimal Control Problem of Deformation and Deflection of a Plate with fracture
  16. Jose Olivencia Quinones, Universidad Nacional de Trujillo - PERÚ De los Momentos a los Cuantos
  17. Jose Atilio Guerrero, Universidad Experimental de Tachira - VENEZUELA, Composition operators on a Banach space of bounded Wiener-variation functions
  18. Jose Luis Sanchez, Universidad Central de Venezuela - VENEZUELA, Controllability of the semilinear Benjamin-Bona-Mahony equation
  19. Juan Montealegre Scoott, Pontificia Universidad Catolica del Perú - PERÚ, Cauchy Problem for a System of a Dispersive Equations
  20. Juan Pablo Borgna, Universidad de Gral. Sarmiento, ARGENTINA,   Existence of Ground-state solutions of 1D Relativistic Schrödinger Equation. A Numerical Method using directly minimization of the energy functional
  21. Jurancy Ereu,Universidad Centro Occidental "Lisandro Alvarado"-UCLA - VENZUELA, Φ-Variacion acotada de funciones de varias variables.
  22. Luis Anzola, U. N. de los Llanos Occ. Ezequiel Zamora(UNELLEZ) - VENEZUELA, On the composition operator on spaces of functions with $\Lambda$-variation in the sense of Waterman
  23. Luis Aguirre Castillo, Universidad Autónoma Metropolitana-Iztapalapa, MÉXICO, Permanence and Stability through Extremal Principles
  24. Maira Valera, Universidad Central de Venezuela - VENEZUELA ,- Efficient and compact closed formulae for 2D- elasticity quadratic boundary elements
  25. Mairene Colina, Universidad Central de Venezuela- VENEZUELA , Parametric and non-parametric estimation of coefficients of the wave equation.
  26. Manuel Garcia Saba, Universidad Nacional de Piura -PERÚ, Numerical solution of nonlinear differential equations using scilab
  27. Maria Sanoja, Universidad Central de Venezuela - VENEZUELA Lipschitzian Composition Operator in the Space kBV [a; b]
  28. Marion Weedermann, Dominican Univesity -  USA,   Mathematical Modeling of Anaerobic Digestion.
  29. Mireya Bracamonte, Universidad Centro Occidental "Lisandro Alvarado"-UCLA- VENEZUELA , Operadores de composicion uniforme continuos en el espacio de phi-variacion n-dimensional en el sentido de Riesz
  30. Neptali Romero, U. Centro-Occidental L. Alvarado - VENEZUELA ,  On the dynamics of  horizontal delay endomorphisms of the plane
  31. Odalis Mejia, Universidad Central de Venezuela - VENEZUELA ,   Uniformly bounded composition operators in the Banach Space of bounded k-variation in the sense of  Riesz.
  32. Raquel Serna Diaz, Universidad Nacional Mayor de San Marcos - PERÚ, Exponencial Decay of Solutións of a Coupled system of Kortewg-de Vries equations with localized damping.
  33. Ruben Agapito, Pontificia Universidad Catolica del Perú - PERÚ, Understanding and Implementing the Multigrid
  34. Zoraida Sivoli, Universidad de los Andes - VENEZUELA ,  Exact controlability of integrodifferential equation wavy con delay
  35. Teodoro Lara, Universidad de los Andes - VENEZUELA ,  Dynamics  of transition of  population interactions.
  36. Yolanda Santiago Avila, Univ. Nacional Mayor de San Marcos - PERÚ, Exponential Rate of Decay of Some Dissipative Systems.
  37. Zorely Jesus, Universidad Central de Venezuela - VENEZUELA ,  Uniformly bounded composition operators in the spaces of funtions of bounded variation in the sense of Schramm
  38. Rocio Caja Rivera, Universidad Nacional Mayor de San Marcos - PERÚ, Cross Diffusion in a pde coupled system with prey predator type  reactions
  39. Martha Timoteo Sanchez, Universidad Nacional Mayor de San Marcos- PERÚ,  Boundary Stabilization for a System of Propagation Sound in a comprenssible fluid.
  40. Emilio Castillo Jimenez, and Willy David Barahona Martínez  Universidad Nacional del callao - PERÚ,  The Transmission problem between an elastic and thermoelastic material with source term.
  41. Gilberto Alva Castillo  and Obidio Rubio Mercedes,  Universidad Privada Antenor Orrego - PERÚ, Simulation of the evolution of the turbulent kinetic energy at the convective boundary layer
  42. Roland Rabanal, Pontificia Universidad Catolica del Perú - PERÚ, Spectral conditions and global phase portrait
  43. Mariel Saez, Pontificia Universidad Catolica de Chile CHILE, Multiple-layer solutions to the Allen-Cahn equation on hyperbolic space
  44. Carlos  Vera, Pontificia Universidad Catolica del Perú - PERÚ, Montecarlo simulation for a solution of a Dirichlet  boundary value problem.
  45. Santiago César Rojas Romero Univ. Nacional Mayor de San Marcos - PERÚ, Fucik curves for a third order boundary value problem
  46. Alfredo Palomino Infante Univ. Nacional Mayor de San Marcos - PERÚ, Modelling the dynamics of the pulsed isolation of essential oil.
  47. Francis Cordova Puma Universidad Federal de Rio de Janiero - BRASIL, On the decay of solutions in interacting continua of solids models