En el estudio de problemas de control o problemas inversos asociados a una EDP, se uti-
lizan propiedades de continuación única (PCU), para las soluciones de las ecuaciones. Este tipo de propiedades están en el centro de los argumentos utilizados para obtener resultados de controlabilidad o estabilidad de sistemas. Sin embargo, no es claro que la solución de alguna discretización del sistema...
In [3] we have introduced the notion of pre-expansivity for cellular automata (CA): it is the
property of being positively expansive on asymptotic pairs of configurations (i.e. configurations that differ in only finitely many positions). Pre-expansivity therefore lies between positive expansivity and pre-injectivity, two important notions of CA theory. It is known [5] that expansivity is...
En esta charla, presentamos resultados para la dinámica que modela la transmisión de una enfermedad sobre una población, la cual se supone que se subdivide en tres compartimentos: Susceptibles(S), Infectados(I) y Recuperados(R), los cuáles viven sobre una región Ω ⊂ R^n , i =1, 2, 3. Mediante técnicas de optimización se estudia la existencia de la solución de un problema inverso relacionado...
A numerical method, based on a machine learning approach, is used to solve an inverse problem involving the Dirichlet eigenfrequencies for the elasticity operator in a bounded domain filled with a composite material. The inhomogeneity of the material under study is characterized by a vector which is designed to control the constituent mixture of homogeneous elastic materials that compose it....
A numerical method based on artificial neural networks is used to solve the inverse Schrödinger equation for a multi-parameter class of potentials. First, the finite element method was used to solve repeatedly the direct problem for different parametrizations of the chosen potential function. Then, using the attainable eigenvalues as a training set of the direct radial basis neural network a...
In two dimensions, we propose and analyze an a posteriori error estimator for the acoustic
spectral problem based on the virtual element method in H(div; Ω). Introducing an auxiliary unknown, we use the fact that the primal formulation of the acoustic problem is equivalent to a mixed formulation, in order to prove a superconvergence result, necessary to despise high order terms. Under the...
In this talk we introduce a new Hybrid High-Order (HHO) method for a linear elliptic
transmission problem in a bounded domain. In HHO the solution of the problem at hand is
approximated by attaching polynomials of degree k to the mesh cells and to their boundaries. Specific element-local operators are then employed to obtain a high-order reconstruction of the solution. Following this...
We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for dissimilar meshes. This type of meshes are common, for instance, when dfferent parts of the domains are triangulated independently, which may generate gaps or overlaps between these triangulations. The method considers an HDG discretization on separate meshes and tie them together through appropriate transmission...
El objetivo central de esta charla es el estudio de la dinámica de fracturas y del daño en la mecánica de rocas. Este es un problema de gran interés en la minería y en particular en la minería subterránea. El objetivo central es estudiar el efecto de la sismicidad en la expansión del daño en macizos rocosos, y de esta forma buscar un modelo matemático que permita explicar el llamado "block...
Over the past few decades, Turing machines have been studied as dynamical systems, focus-ing on their behavior over their results. Noteworthy results concerning topological and dynam-ical properties were established, as the existence and undecidability of Topological Transitivity in Turing machines with moving head, and Topological Minimality in Turing machines with moving tape. Both...
We consider the nonhomogeneous incompressible Magnetohydrodynamic equations in a thin domain Ω := R 2 × (0, ep), with. ep ∈ (0, 1], and show the global existence of strong solutions. In addition, we prove that, as ep → 0 + , the velocity and magnetic field tends to vanish away from the initial time.
We extend the spectral regularity criteria of the Prodi-Serrin kind for the Navier-Stokes
equations in a torus to the MHD equations. More precisely, the following is established: for any N > 0, let x_N and y_N be the sum of all spectral components of the velocity and magnetic field whose wave numbers possess absolute value greater that N; then, it is possible to show that for any N the...
Iâll introduce this context to some levels of chaoticity in group actions, at the local level,
seeking to verify that some classic properties are fulfilled for a given group. Afterward, it is
proposed to study the relationship between notions of Chaos (in a distributional and Li-Yorke sense) with the property of undecidability. Finally, some examples of this will be given.
Conversatorio Programa Copernicus. La charla se realizara en el Sport Burger Bar, Avenida Argentina 295, Chillan
This study considers the interaction between a free vorticity wave packet and a rapidly
rotating vortex in the slowly-evolving regime, a long time after the initial, unsteady, and strong interaction. The interaction starts when the amplitude modulated neutral mode enters resonance with the vortex on a spiralling critical surface, where the phase angular speed is equal to the rotation...
