# Seminario CAPDE

2017-05-08
4:00pmhrs.
María Medina. Pontificia Universidad Católica de Chile
A Mixed Fractional Problem. Moving The Boundary Conditions
Sala 2, Facultad de Matemáticas, PUC
Abstract:
A natural question when one considers the mixed eigenvalue problem for the Laplacian (zero DIrichlet condition in D and Neumann homogeneous in N where $\Omega$ is a Lipschitz bounded domain in $R^N$ and D, N are disjoint submanifolds of ∂Ω) is whether the configuration of the sets D and N determines the behavior of u. Is it similar to the solution of the Dirichlet problem when N is small? or does it behave like the Neumann eigenfunction when N is large? Several authors have shown results where different configurations of D and N provide very different behaviors of u (see for example [Colorado & Peral 2003, Denzler 1999]) depending on the size of the sets, but also on their location.

In this talk we will try to understand the analogous non local problem where N and D are now two open sets of $R^N\Omega$. As we will see, the fact that the boundary now happens to be the whole $R^N\Omega$ instead of ∂Ω completely changes the possible configurations of the sets (one can even have both sets of unbounded measure). The purpose of this talk will be to understand what “a small boundary set” means here, and to analyze how D and N can move to recover the classical results.

This is a joint work with T. Leonori, I. Peral, A. Primo and F. Soria, that can be found at https://arxiv.org/pdf/1702.07644.pdf.
http://capde.cl/scientific-activities-2/
2017-05-08
5:00pmhrs.
Erwin Topp Paredes. Universidad de Santiago de Chile
Parabolic Equations With Caputo Time Derivative
Sala 2, Facultad de Matemáticas, PUC
Abstract:
In this talk we report results presented in [Topp & Yangari 2017] about well-posedness of fully nonlinear Cauchy problems in which the time derivative is of Caputo type. We address this question in the framework of viscosity solutions, obtaining the existence via Perron’s method, and comparison for bounded sub and supersolutions by a suitable regularization through inf and sup convolution in time. As an application, we prove the steady-state large time behavior in the case of proper nonlinearities and provide a rate of convergence by using the Mittag-Leffler operator.
http://capde.cl/scientific-activities-2/
2016-11-21
16:00hrs.
Juan Diego Dávila. Universidad de Chile
Finite Time Blow-Up For The Harmonic Map Flow In 2 Dimensions
Sala 5
Abstract:
We describe precisely the finite time blow up behavior of some solutions of the harmonic map flow in 2 dimensions with values into the sphere, in a nonradial situation. One important quantity is the rate of blow up, which was established rigorously only in the 1-corrotational symmetric class by Raphael and Schweyer. This is joint work with Manuel del Pino (Universidad de Chile) and Juncheng Wei (University of British Columbia).
2016-11-21
17:00hrs.
Luis Fernando López. Università Degli Studi Roma Tre
The Mean Field Equation In High Dimensions
Sala 5
Abstract:
In this talk we present an n-dimensional version of the well known 2D mean field equation. We exhibit a special set of solutions to the model and prove a nondegeneracy property associated with the linearization of the operator. Such property is used to study the behavior of blowing-up families of solutions. This phenomenon is inspired in related models, where the lack of compactness of the Sobolev embedding is closely related to the concentration of solutions. This is a joint work with Pierpaolo Esposito.
2016-09-05
16:00hrs.
Karina Vilches. U. Católica del Maule
Simultaneous Blow-Up For Two Species Patlack-Keller-Segel System In $\mathbb R^2$
Sala de seminarios del 5to. piso del Departamento de Ingeniería Matemática DIM, U. de Chile
2016-09-05
17:10hrs.
Gianmarco Sperone. Dim U. Chile
Further Remarks On The Luo-Hou's Ansatz For a Self-Similar **solution To The 3D Euler Equations
Sala de seminarios del 5to. piso del Departamento de Ingeniería Matemática DIM, U. de Chile
Abstract:
It is shown that the self-similar ansatz proposed by T. Hou and G. Luo to describe a blow-up solution of the 3D axisymmetric Euler equations leads, without assuming any asymptotic condition on the self-similar profi les, to an over-determined system of partial differential equations that produces two families of solutions: a class of trivial solutions in which the vorticity field is identically zero, and a family of solutions that blow-up immediately, where the vorticity field is governed by a stationary regime.
In any case, the analytical properties of these solutions are not consisent with the numerical observations reported by T. Hou and G. Luo. Therefore, this result is a refi nement of the previous work published by D. Chae and T.-P. Tsai on this matter, where the authors find the trivial class of solutions under a rather unjusti fied decay condition of the blow-up profiles.

2016-08-08
Duvan Henao. P. Universidad Católica de Chile
Existence Theorems For Geometrically Nonlinear Models Of Nematic Elastomers
Sala 5 de la Facultad de Matemáticas a las 17:00 Hrs.
2016-08-08
Mariel Sáez. P. Universidad Católica de Chile
Fractional Laplacians And Extension Problems: The Higher Rank Case (Joint With M.m. Gonzalez)
Sala 5 de la Facultad de Matemáticas entre las 16:00 Hrs.
2016-06-05
About Hardy-Sobolev, Moser-Trudinger And Isoperimetric Inequalities With Densities
Sala 5 de la Facultad de Matemáticas a las 17:00 Hrs.
2016-05-02
María Medina. Pontificia Universidad Católica de Chile
The Effect Of The Hardy Potential In Some Calderón-Zygmund Properties For The Fractional Laplacian
Sala 2 Facultad de Matemáticas, P.U.C. a las 17:00 Hrs.
2016-04-25
Carlos Román. Université Pierre Et Marie Curie - Paris Vi,
On The First Critical Magnetic Field In The Three-Dimensional Ginzburg-Landau Model Of Superconductivity
Sala de seminarios D.I.M. (5to piso), U. de Chile a las 17:00 Hrs.
2016-04-18
Michel Chipot. Universität Zürich
Nonhomogeneous Boundary Value Problems For The Stationary Navier-Stokes Equations In Two-Dimensional Domains With Semi-Infinite Outlets
Sala de seminarios del Departamento de Ingeniería Matemática de la Universidad de Chile 5º piso, Beauchef 851, Edificio Norte a las 17:00 Hrs.
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
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.
2015-09-30
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.
2015-09-14
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