Noticias en español
Variational Approach for the Singular Perturbation Domain Wall Coupled System.
Abstract: In this talk, I will present results on a singular perturbation problem modeling domain walls. I will discuss the existence of solutions both when the perturbation parameter is non-zero and when it is set to zero (Thomas-Fermi approximation), demonstrating their continuous connection as the parameter approaches zero. Finally, I will show that the behavior of one of the variables can be modeled by a Painlevé II equation in the limit, by the use of an appropriate change of variables.
Read MoreSharp Fourier restriction over finite fields.
Abstract: Fourier sharp restriction theory has been a topic of interest over the last decades. On the other hand, efforts have been made in order to develop the theory of Fourier restriction over finite fields. In this talk, we will present some recently made developments (in a joint work with Diogo Oliveira e Silva) in the intersection of these two topics.
Read MoreBounds on the approximation error for Deep Neural Networks applied to dispersive models: Nonlinear waves.
Abstract: In this talk we present a comprehensive framework for deriving rigorous and efficient bounds on the approximation error of deep neural networks in PDE models characterized by branching mechanisms, such as waves, Schrödinger equations, and other dispersive models. This framework utilizes the probabilistic setting established by Henry-Labordère and Touzi. We illustrate this approach by providing rigorous bounds on the approximation error for both linear and nonlinear waves in physical dimensions d = 1, 2, 3, and analyze their respective computational costs starting from time...
Read MoreOn the nonexistence of NLS breathers.
Abstract: In this talk, we will show a proof of the nonexistence of breather solutions for NLS equations. By using a suitable virial functional, we are able to characterize the nonexistence of breather solutions by only using their inner energy and the power of the corresponding nonlinearity of the equation. We extend this result for several NLS models with different power nonlinearities and even the derivative NLS equation.
Read MoreDelaunay-type compact equilibria in the liquid drop model
Speaker: Manuel del Pino Department of Mathematical Sciences, University of Bath, UK Date: Thursday 11th July, 2024 at 4:15 pm Santiago time Abstract: — Venue: Sala de seminarios DIM, 5th floor, Beauchef 851 / Online via Zoom Chair: Gabrielle Nornberg PDE Seminars About Manuel del Pino Manuel del Pino currently holds the position of Professor in the Department of Mathematical Sciences at the University of Bath, UK. In 2018, he was honored with a Royal Society Research Professorship, the Society’s top research award, allowing exceptional scientists to focus on research by relieving...
Read MoreA variational and numerical approach to model inverse problems applied in subduction earthquakes.
Abstract: This talk presents a mixed variational formulation for the problem of the elasticity equation with jump conditions in an interface with the purpose of modeling subduction earthquakes by introducing the concept of coseismic jump. For this new problem, we introduced an optimal control problem that seeks to recover the coseismic jump from boundary observations. Both problems can be discretized by applying mixed finite elements. Synthetic results applied to a realistic context will be presented. Finally, we analyze some improvements for the numerical discretization and preliminary...
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