Noticias en español
Delaunay-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...
Read MoreFrom non-local to local Navier-Stokes equations
Resumen: Inspired by some experimental (numerical) works on fractional diffusion PDEs, we develop a rigorous framework to prove that solutions to the fractional Navier-Stokes equations, which involve the fractional Laplacian operator, converge to a solution of the classical case. Precisely, in the setting of mild solutions, we prove uniform convergence in both the time and spatial variables and derive a precise convergence rate, revealing some phenomenological effects.
Read MoreA qualitative analysis of an Aβ-monomer model with inflammation processes for Alzheimer’s disease.
Abstract: We introduce and study a new model for the progression of Alzheimer’s disease incorporating the interactions of A_beta-monomers, oligomers, microglial cells and interleukins with neurons through different mechanisms such as protein polymerization, inflammation processes and neural stress reactions. In order to understand the complete interactions between these elements, we study a spatially-homogeneous simplified model that allows to determine the effect of key parameters such as degradation rates in the asymptotic behavior of the system and the stability of equilibriums. We...
Read MoreAsymptotic stability of small solitary waves for the one-dimensional cubic-quintic Schrödinger equation.
Abstract: I will present two results on the asymptotic stability of small solitary waves for the one-dimensional cubic-quintic Schrödinger equation. The first result concerns the focusing-defocusing double power nonlinearity, for which the linearized operator around the small solitary waves has no internal mode. The second result concerns the more delicate case of the focusing-focusing double power nonlinearity, for which the linearized operator around the small solitary waves actually has an internal mode. The internal mode component of the solution is controlled by checking explicitly a...
Read MoreUndestanding the APS boundary condition for the zero modes of the Dirac operator.
Abstract: How many zero modes (states with zero energy) are there of the Dirac operator with magnetic field in two dimensions? This question was answered by Aharonov and Casher in 1979 for the case of plane. They showed that this number is given by the flux of the magnetic field, more precisely the integer part of it. Moreover, the zero modes are chiral, aligning with the direction of the magnetic field. We investigate the same problem for the case of a plane wih holes considering the Atiyah–Patodi–Singer (APS) boundary condition (BC). This BC was introduced by APS in their...
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