Seminario CAPDE


2016-04-12
Miguel Ángel Alejo. Universidade Federal de Santa Catarina
Stability of Mkdv Breathers and Numerical Results
Sala de seminarios del Departamento de Ingeniería Matemática de la Universidad de Chile 5º piso, Beauchef 851, Edificio Norte a las 15:00 Hrs.
2016-01-13
André de Laire. U. Lille
Global Well-Posedness for a Nonlocal Gross-Pitaevskii Equation With Nonzero Condition At Infinity
Sala de seminarios del 5to piso del DIM a las 17:05 Hrs.
2016-01-13
Sylvain Ervedoza. U. Toulouse
Local Exact Controllability for Compressible Navier-Stokes Equations Around Constant Trajectories
Sala de seminarios del 5to piso del DIM a las 16:00 Hrs.
2015-10-19
Rémy Rodiac. P. Universidad Católica de Chile
Ginzburg-Landau Type Problems With Prescribed Degrees on The Boundary
Sala 5 Facultad de Matemáticas a las 16:00 Hrs.
2015-10-19
Yannick Sire. Johns Hopkins University
Bounds on Eigenvalues on Riemannian Manifolds
Sala 5 Facultad de Matemáticas UC a las 17:00 Hrs
2015-09-30
Paolo Caldiroli. Universitá Di Torino
Isovolumetric and Isoperimetric Inequalities for a Class of
Sala 1 de la Facultad de Matemáticas de la PUC a las 16:00 Hrs.
2015-09-30
Denis Bonhere. Université Libre de Bruxelles
On The Higher Dimensional Extended Allen-Cahn Equation
Sala 1 Facultad de Matemática PUC a las 17:00 Hrs.
2015-09-14
Rafael Benguria. Departamento de Física de la P. Universidad Católica de Chile
The Brezis-Nirenberg Problem on S^n, in Spaces of Fractional Dimension
Sala de seminarios del 5to piso del Departamento de Ingeniería de la Universidad de Chile
2015-08-24
Claudio Muñoz. (Dim-Cmm)
Asymptotic Stability of Solitons of The High Dimensional Zakharov-Kuznetsov Equation
Sala de Seminarios del Depto. de Ingeniería Matemático, 5to piso de Beauchef 851 - 16:00 Hrs.
2015-05-18
Weiwei Ao. Department of Mathematics, University of British Columbia, Vancouver
Refined Finite-dimensional Reduction Method and Applications to Nonlinear Elliptic Equations
Sala 1 de la Facultad de Matemáticas de la Universidad Católica - 16:50 Hrs.
Abstract:
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.
2015-05-18
Jun Yang. School of Mathematics and Statistics, Central China Normal University
Vortex structures for maps from pseudo-Euclidean spaces
Sala 1 de la Facultad de Matemáticas de la Universidad Católica -16:00 hrs.
Abstract:
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.
2015-04-27
Disson Dos Prazeres. CMM Universidad de Chile
The Hilbert´s Nineteenth Problem
Sala de seminarios del Departamento de Ingeniería Matemática de la Universidad de Chile 5º piso, Beauchef 851, Edificio Norte 15:00 Hrs.
2015-04-27
Erwin Topp. Utfsm
Large Solutions for Non Uniformly Elliptic Semilinear Equations
Sala de seminarios del Departamento de Ingeniería Matemática de la Universidad de Chile 5º piso, Beauchef 851, Edificio Norte -16:15
2012-12-06
Martin Man-Chun Li. University of British Columbia
Minimal surfaces with free boundary
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - 16:00 Hrs.
Abstract:
Abstract: Minimal surfaces have been a rich object of study in various fields of mathematics, including geometry, analysis and PDE. In this talk, I will describe a natural free boundary problem for minimal surfaces. After a brief survey on some classical results about minimal surfaces (and minimal submanifolds in general) with free boundary, I will describe some recent existence and regularity results for embedded solutions. I will also discuss a compactness result (joint work with A. Fraser) for the moduli space of embedded free boundary minimal surfaces in the unit ball, and its relation to the spectrum of the Dirichlet-to-Neumann operator.

2011-08-07
David Ruiz. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada
Existence of solutions for the Toda System via variational methods
Sala 3 (Sector Postgrado) Facultad de Matemáticas - 16:00 Hrs.
Abstract:
In this talk we study the existence of solutions of a Toda System on a compact surface. The bubbling behavior, as well as an analogue of the Moser-Trudinger inequality, have been given by Jost, Lin and Wang. However, apart from the trivial coercive cases, there is no much information on the existence of solutions.
Our approach is variational, and we look for solutions as critical points of the associated energy functional. In order to do so, a detailed description of the low sublevels of the functional is needed. This is done by a convenient definition of center of mass and degree of concentration of a $L 1 $ function, together with an apropriate version of the Moser-Trudinger inequality.
This is joint work with Andrea Malchiodi (SISSA, Italy).

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2011-08-07
David Ruiz. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada
Existence of solutions for the Toda System via variational methods
Sala 3 (Sector Postgrado) Facultad de Matemáticas, 16:00 Hrs.
Abstract:
In this talk we study the existence of solutions of a Toda System on a compact surface. The bubbling behavior, as well as an analogue of the Moser-Trudinger inequality, have been given by Jost, Lin and Wang. However, apart from the trivial coercive cases, there is no much information on the existence of solutions.
Our approach is variational, and we look for solutions as critical points of the associated energy functional. In order to do so, a detailed description of the low sublevels of the functional is needed. This is done by a convenient definition of center of mass and degree of concentration of a $L 1 $ function, together with an apropriate version of the Moser-Trudinger inequality.
This is joint work with Andrea Malchiodi (SISSA, Italy).

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2011-08-07
Duvan Henao Manrique. Pontificia Universidad Católica de Chile
Isoperimetric inequalities and cavity interactions in nonlinear elasticity
Sala 3 (Sector Postgrado) 17:00 Hrs
Abstract:
In this joint work with Sylvia Serfaty (LJLL, Univ. Paris VI) we consider the problem of cavitation in nonlinear elasticity, or the formation of macroscopic cavities in elastic materials from microscopic defects, when subjected to large tension at the boundary. The main goal is to determine the optimal locations where the body prefers the cavities to open, the preferred number of cavities, their optimal sizes, and their optimal shapes. To this aim it is necessary to analyze the elastic energy of an incompressible deformation creating multiple cavities, in a way that accounts for the interaction between the cavitation singularities. Based on the quantitative isoperimetric inequality, as well as on new explicit constructions of incompressible deformations creating cavities of different shapes and sizes, we provide energy estimates showing that, for certain loading conditions, there are only the following possibilities:
- only one cavity is created, and if the loading is isotropic then it is created at the centre
- multiple cavities are created, they are spherical, and the singularities are well separated
- there are multiple cavities, but they act as a single spherical cavity, they are considerably
distorted, and the distance between the cavitation singularities must be of the same order as the size of the initial defects contained in the domain. In the latter case, the formation of thin structures between the cavities is observed, reminiscent
of the initiation of ductile fracture by void coalesence.


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