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
16h
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.
16h50
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
15h:15
Hernan Castro (Universidad de Talca)
Ecuaciones de Sturm-Liouville singulares
Abstract
16h30
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.