Category Archives: Uncategorized

Radio Duna: Interview to Omar Gil

Omar Gil, screenwriter of “Primos entre sí”, the theater play sponsored by Capde, talks live in radio about the importance of bringing mathematics to the schoolrooms. He pointed out that this field of knowledge helps people to “understand better the world”. He also explains the need to accept mistakes during the process of learning.

Source: Radio Duna


Monday August 3

No seminar (Inverse Problems in the Physical Sciences, IP-Phys2015, see website

Monday August 10


Didier Pilod (UFRJ, Brasil) 

Dispersive perturbations of Burgers and hyperbolic equations 




Monday August 24


Claudio Muñoz (DIM-CMM) 

Asymptotic Stability of solitons of the high dimensional Zakharov-Kuznetsov equation 

In this talk I will discuss a recent work with R. Cote, D. Pilod and G. Simpson, where we considered solitons of the high dimensional Zakharov-Kuznetsov equation, a model of plasma ions in Physics. In particular, we prove that solitons are strongly asymptotically stable in the energy space, in a particular region of the plane determined by natural geometric and dispersive constraints. In proving this result we extend to the high dimensional case several tools coming from the one-dimensional setting (generalized KdV equations), introduced by Martel and Merle. However, some new difficulties arise when consider the dimension greater than two, in particular when proving required spectral properties, decay estimates, and the compactness in time of the asymptotic solution.




Monday July 6


Jianfu Yang (TBA) 

Equations involving fractional Laplacian operator: Compactness and applications 



Huyuan Cheng (TBA) 

Boundary blow-up solutions of fractional equations in a measure framework 


Monday July 13


Anna Kazeykina (Universidad Paris-Sud, France) 

On the behaviour of solutions for the Novikov-Veselov equation 

The Novikov-Veselov equation is a 2-dimensional generalization of the renowned Korteweg-de Vries equation integrable via the Inverse Scattering Transform (IST) for the 2-dimensional stationary Schrodinger equation. In this talk we will present recent results on the behaviour of solutions to the Novikov-Veselov equations: local well-posedness results, existence and absence of solitons, large-time behaviour, blow-ups etc. A part of results is obtained via IST techniques; for other results we make use of techniques of the theory of dispersive PDEs. 

Monday July 27

No seminar (XVIII International Congress on Mathematical Physics, see website)


Wednesday May 13, 12h, Sala Seminario 5to. piso. (Notar fecha y hora especiales) (Seminario anulado) 

Yvan Martel (Ecole Polytechnique) 

Survey on blow up for the critical generalized Korteweg-de Vries equation 

We will review recent results with Frank Merle and Pierre Raphael (and also partly with Kenji Nakanishi) on blow up for critical generalized Korteweg-de Vries equation, and more generally on the classification of solutions close to the solitons.


Monday May 18, PUC, sala 1 Matematicas


Jun Yang (Central China Normal University) 

Vortex structures for maps from pseudo-Euclidean spaces 

For some geometric flows (such as wave map equations, Schrödinger flows) from pseudo-Euclidean spaces to a unit sphere contained in a three dimensional Euclidean space, we construct solutions with various vortex structures(vortex pairs, vortex circles and helices). The approaches base on the transformations associated with the symmetries of the nonlinear problems, which will lead to two dimensional elliptic problems with resolution theory given by the finite dimensional Lyapunov-Schmidt reduction method in nonlinear analysis. 


Weiwei Ao (University of British Columbia) 

Refined Finite-dimensional Reduction Method and Applications to Nonlinear Elliptic Equations 

I will talk the refined finite dimensional reduction method and its application to nonlinear elliptic equations. We use this refined reduction method to get optimal bound on the number of interior spike solutions of the singularly perturbed Neumann problem as well as the boundary spike solutions. I will also talk about the entire solutions for nonlinear Schrodinger equations. 

Monday May 25


Hernan Castro (Universidad de Talca) 

Ecuaciones de Sturm-Liouville singulares 



Eduardo Cerpa (UTFSM) 

Control de la ecuación de Korteweg-de Vries 

En esta charla introduciremos el concepto de controlabilidad de ecuaciones en derivadas parciales. En particular, estudiaremos el control frontera de la ecuación de Korteweg-de Vries y veremos cómo el dominio en donde la ecuación es estudiada puede influir en las propiedades del sistema. Nos interesaremos en algunos casos en donde la nolinealidad de la ecuación es crucial para demostrar su controlabilidad. 

Wednesday May 27, 12h, Sala Seminario 5to. piso. (Notar fecha y hora especiales) 

Marcelo Amaral (Unilab-Brazil) 

Transmission problems on free interfaces 

We study transmission problems with free interfaces from one random medium to another. Solutions are required to solve distinct partial differential equations, L + and L -�, within their positive and negative sets respectively. A corresponding flux balance from one phase to another is also imposed. We establish existence and L infinity bounds of solutions. We also prove that variational solutions are non-degenerate and develop the regularity theory for solutions of such free boundary problems.

16th  March


Nicolas Vauchelet (Universidad Paris 6) 

Mathematical study of a cell model for tumor growth : travelling front and incompressible limit 

We consider mathematical models at macroscopic scale to describe tumor growth. In this view, tumor cells are considered as an elastic material subjected to mechanical pressure. Two main classes of model can be encountered: those describing the dynamics of tumor cells density and those describing the dynamic of the tumor thanks to the motion of its domain. These latter models are free boundary problem. We will show that such free boundary problem of Hele-Shaw type can be derived thanks to an incompressible limit from models describing the dynamics of cells density. Moreover, for this model we study the existence of travelling waves, allowing to describe the spread of the tumor. 


Pierpaolo Esposito (Universidad de Roma Tre) 

Equilibria of point-vortices on closed surfaces 

I will discuss the existence of equilibrium configurations for the Hamiltonian point-vortex model on a closed surface. Its topological properties determine the occurrence of three distinct situations, corresponding topologically to the sphere, to the real projective plane and to the remaining cases. As a by-product, new existence results are obtained for the singular mean-field equation with exponential nonlinearity. 

Joint work with T. D’Aprile. 


Oscar Agudelo (University of West Bohemia) 

Singularly perturbed Allen-Cahn equation with catenoidal nodal sets 

In this lecture we review some recent results concerning existence and asymptotic behavior of solutions to the singularly perturbed problem 

\alpha^2 \Delta u + u(1-u^2)=0, in Omega 

where \Omega \subset \mathbb{R}^N is either a smooth bounded domain or the entire space and N\geq 2. We take advantage of the deep connection between the equation above and the theory of minimal surfaces to study asymptotic profiles of the solutions. Particular attention is paid to solutions with catenoidal nodal set. 

From 30th March to 2nd April

Cursillo “On vortex dynamics in two-dimensional or three-dimensional incompressible flows”,

por Evelyne Miot (CNRS and Ecole Polytechnique, investigadora invitada CMM) 

– Lecture 1 (Lunes 30 Marzo, 16h-17:30h, Sala Seminario 5to. piso):
Vortices in incompressible fluids. 

In this first lecture we will consider the Euler equations governing the motion of incompressible fluids, in particular in a two-dimensional setting. We will focus on the vortex solutions and present Marchioro and Pulvirenti’s result on the derivation of the point vortex system from the 2D Euler equations. We will also briefly mention the vortex dynamics in other related equations (the Navier-Stokes equation and the Gross-Pitaevskii equation). 

– Lecture 2 (Miércoles 1 Abril, 12h-13:30h, Sala Seminario 5to. piso)
Convergence of the point vortex system to the 2D Euler equation. 

This lecture will explore more in detail the connection between the discrete model, described by the point vortex system, and the continuous fluid dynamics given by the Euler equation. We will show how the results by Goodman, Lowengrub and Hou and Schochet ensure that the point vortex system is a good approximation of the Euler equation when the number of vortices is large. 

– Lecture 3 (Jueves 2 Abril, 14:30h-16h, Sala Seminario 7mo. piso):
Vortex filaments. 

We will study the analogous notion of point vortices in three dimensions, namely the vortex filaments. We will explain the formal derivation leading to the binormal curvature flow equation governing the motion of one single vortex filament. We will also relate the binormal curvature flow equation and the cubic 1D Schrödinger equation via the Hasimoto transform. Finally we will present a system of simplified equations proposed by Klein, Majda and Damodaran to describe the interaction of several almost parallel vortex filaments. 

Fethi Mahmoudi

PhD in Mathematics, Université Paris XII, France (2005)
Master in Numerical Analysis and Partial Differential Equations, Université Pierre et Marie Curie, France (2001)

Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (CMM)
Facultad de Ciencias Físicas y Matemáticas
Universidad de Chile


Research area
Geometric Analysis, Nonlinear Partial Differential Equations, Differential Geometry, Riemannian Geometry.

+56 2 2978 0512
Beauchef 851, North Building, 7th floor, office 707. Santiago, Chile.

Mónica Musso

PhD in Mathematics, University of Pisa, Italy (1998)
Bachelor degree in Mathematics, University of Torino, Italy (1992)

Pontificia Universidad Católica de Chile

Assistant professor

Research area
Nonlinear Analysis

+562 2354 5816
Vicuña Mackenna 4860. Santiago, Chile

Ignacio Guerra

Ph D in Engineering Mathematical Sciences, Technische Universiteit Eindhoven, Holland (2003)
Civil Mathematical Engineering, Universidad de Chile (1998)

Universidad Santiago de Chile

Associated Professor

Research area
Partial Differential Equations

+56 2 271 82055
Las Sophoras 173, Santiago, Chile