Speaker: Felipe Chaves-Silva

Universidade Federal da Paraíba

Date: Monday, September 4th, 2023 at 12 Santiago time

Venue:  Sala de Seminarios, 5th floor, Beauchef 851 / Online via Zoom
Chair: Rayssa Caju

Speaker: Axel Osses 

DIM- CMM, Universidad de Chile

Date: Monday, August 21st, 2023 at 12 Santiago time

Venue: Online via Zoom / Sala de Seminarios, 5th floor, Beauchef 851
Chair: Rayssa Caju

Speaker: Sameer Iyer

University of California – Davis, USA.

Date: Monday, August 14th, 2023 at 12 Santiago time

Venue: Online via Zoom / Sala de Seminarios, 5th floor, Beauchef 851
Chair: Rayssa Caju

Speaker: Ricardo Freire

DIM CMM – Universidad de Chile

Date: Monday, August 7th, 2023 at 12 Santiago time

Abstract: We consider the long-time dynamics of large solutions to a special class of evolution equations. Using virial techniques, we describe regions of space where every solution in a suitable Sobolev space must decay to zero along sequences of times. Moreover, in the case of interior regions, we prove decay for a sequence of times. The classes of nonlocal dispersive equations which we will treat are as follows:

Venue: Online via Zoom / Sala de Seminarios, 5th floor, Beauchef 851
Chair: Rayssa Caju

Speaker: Jaime Ortega

DIM CMM – Universidad de Chile

Date: Monday, July 10, 2023 at 12 Santiago time

Abstract: Es bien conocido que las Propiedades de Continuación Única juegan un importante papel en el estudio de los problemas de controlabilidad y problemas inversos. También es natural preguntarse que sucede con las discretizaciones de las EDP y sus propiedades. En esta charla mostraremos que al considerar la discretización, en diferencias finitas, de operadores diferenciales, este tipo de propiedades pierden su validez, por lo que es válido preguntarse si resultados de controlabialidad, identificabilidad y estabilidad en los problemas inversos siguen siendo válidos en el caso discreto. Aquí damos una respuesta afirmativa a esta pregunta, pero la validez de estos resultados dependen de ciertos parámetros relacionados con el tamaño de la malla.

Venue: Online via Zoom / Sala de Seminarios, 5th floor, Beauchef 851
Chair: Rayssa Caju

Speaker: Khawla Msheik

Université Lyon 1 – Institut Camille Jordan, France

Date: Monday, July 3, 2023 at 12 Santiago time

Abstract: We propose in this work a new system of equations modeling Tsunamis. It is a coupled system accounting for both water compressibility and viscoelasticity of the earth. Adding these latter physical effects is responsible for the closest-to-reality time arrival predictions (among existing models), capturing the negative peak before the main wave hump, and the exhibition of the negative dispersion phenomena. This comes in remarkable agreement with previous experiments and studies on the topic. The system is also delivered in a relatively simple mathematical structure of equations that is easy to solve numerically. Further well posedness results are also investigated.

Venue: Online via Zoom / Sala de Seminarios, 5th floor, Beauchef 851
Chair: Rayssa Caju

Speaker: Victor Cañulef 

CMM – Universidad de Chile

Date: Monday, June 19, 2023 at 12 Santiago time

Abstract: The hydrostatic Euler equations are derived from the incompressible Euler equations by means of the hydrostatic approximation. Among the different stability criteria that arise in the study of linear stability for the incompressible Euler equations, we can mention Rayeligh’s stability criterion, which gives rise to the local Rayleigh condition. Linear and nonlinear instability of the hydrostatic Euler equations around certain shear flows is well-known, as well as the finite time blow-up of certain solutions that do not satisfy the local Rayleigh condition. On the other hand, local existence, uniqueness and stability has been established in Sobolev spaces under the local Rayleigh condition. In this talk I will present new features of the \(H^4\) solution to the hydrostatic Euler equations under the local Rayleigh condition; under certain assumptions, we establish the dichotomy between the breakdown of the local Rayleigh condition and the formation of singularities. Additionally, we get necessary conditions for global solvability in Sobolev spaces. As a byproduct, we show the $x-$independence of stationary solutions. Our proof relies on new monotonicity identities for the solution to the hydrostatic Euler equations under the local Rayleigh condition.

Venue: Online via Zoom / Sala John Von Neumann, 7th floor, Beauchef 851
Chair: Rayssa Caju

Speaker: Disson dos Prazeres

Universidade Federal de Sergipe (Brasil)

Date: Monday, June 12, 2023 at 12 Santiago time

Abstract: We derive Cordes-Nirenberg type results for nonlocal elliptic equations with deforming kernels using a compactness method.Under a natural integrability assumption for the Monge-Ampere solution, we are able to prove a stability lemma that allows the ellipticity class to vary. As a consequence, we get that the limit equation, up to a rotation, behaves like rough fractional Laplacians where the known regularity theory for this class of equation can be applied.

Joint work with A. Sobral and J.M. Urbano.

Venue: Online via Zoom / Sala de Seminarios, 5th floor, Beauchef 851
Chair: Rayssa Caju

Speaker: Marcela Cárdenas

Universidad Andrés Bello (Chile)

Date: Monday, June 5, 2023 at 12 Santiago time

Abstract:In this talk we discuss the geometrization of 1+1 integrable systems included in the AKNS integrable system, which contains the Korteweg de-Vries (KDV), modified KDV, sine-Gordon and non-linear Schrödinger equations. This is possible through the construction of a broad class of asymptotic conditions for the gravitational field in three dimensions, reproducing the properties of the AKNS dynamics. We study the consistency, asymptotic symmetry algebra and integrability properties of these novel boundary conditions.

Venue: Online via Zoom / Sala de Seminarios, 5th floor, Beauchef 851
Chair: Rayssa Caju

Speaker: Gianmarco Sperone

Politecnico di Milano

Date: Monday, May 22, 2023 at 12 Santiago time

Abstract: The steady motion of a viscous incompressible fluid in an obstructed finite pipe is modeled through the Navier-Stokes equations with mixed boundary conditions involving the Bernoulli pressure and the tangential velocity on the inlet and outlet of the tube, while a transversal flux rate F is prescribed along the pipe. Existence of a weak solution to such Navier-Stokes system is proved without any restriction on the data by means of the Leray-Schauder Principle, in which the required a priori estimate is obtained by a contradiction argument based on Bernoulli’s law. Through variational techniques and with the use of an exact flux carrier, an explicit upper bound on F (in terms of the viscosity, diameter and length of the tube) ensuring the uniqueness of such weak solution is given. This upper bound is shown to converge to zero at a given rate as the length of the pipe goes to infinity. In an axially symmetric framework, we also prove the existence of a weak solution displaying rotational symmetry.

Venue: Online via Zoom / Sala de Seminarios, 5th floor, Beauchef 851
Chair: Rayssa Caju