Noticias en español
Ecuaciones integro-diferenciales y procesos semi-markovianos.
Resumen: En esta charla mostraremos cómo algunas generalizaciones de la derivada fraccionaria en tiempo en el sentido de Caputo pueden ser usadas para estudiar propiedades de ciertos procesos semi-markovianos.
Read MoreInverse scattering for critical semilinear wave equations.
Abstract: In inverse scattering ione attempts to find the properties of a medium by making remote observations. It has applications in physics, geophysics, medical imaging, non-destructive evaluation of materials. Radar and sonar are examples of inverse scattering methods that are used routinely nowadays. In this case we consider the inverse problem of determining the nonlinearity for critical semilinear wave equations. This is joint work with A, Sa Barreto and Y. Wang.
Read MoreMultiplicidad de soluciones por cambios de magnitud.
Abstract: Estudiaremos las soluciones radialmente simétricas del problema Δu+f(u)=0,x∈RN,N>2,lim|x|→∞u(x)=0. Veremos que podemos generar nuevas soluciones del problema si introducimos cambios bruscos en la magnitud de la función f. Usando esto construiremos funciones f, definidas por partes, tales que el problema tiene cualquier número pre-determinado de soluciones.
Read MoreTime periodic solutions for 3D quasi-geostrophic model.
Abstract: The aim of this talk is to study time periodic solutions for 3D inviscid quasigeostrophic model. We show the existence of non trivial simply-connected rotating patches by suitable perturbation of stationary solutions given by generic revolution shapes around the vertical axis. The construction of those special solutions are done through bifurcation theory. In general, the spectral problem is very delicate and strongly depends on the shape of the initial stationary solutions. More specifically, the spectral study can be related to an eigenvalue problem of a self-adjoint compact...
Read MoreLong-time behavior of a sexual reproduction model under the effect of strongly convex selection.
Abstract: The Fisher infinitesimal model is a widely used statistical model in quantitative genetics that describes the propagation of a quantitative trait along generations of a population subjected to sexual reproduction. Recently, this model has pulled the attention of the mathematical community and some integro-differential equations have been proposed to study the precise dynamics of traits under the coupled effect of sexual reproduction and natural selection. Whilst some partial results have already been obtained, the complete understanding of the long-time behavior is essentially...
Read MoreOn large solutions for fractional Hamilton-Jacobi equations.
Abstract: In this talk I will report some multiplicity results for large solutions of fractional Hamilton-Jacobi equations posed on a bounded domain, subject to exterior Dirichlet conditions. We construct large solutions using the method of sub and supersolutions, following the classical approach of J.M. Lasry and P.L. Lions for second-order equations with subquadratic gradient growth. We identify two classes of solutions: the one coming from the natural scaling of the problem; and a one-parameter family of solutions, different from the previous, which can be formally described as a...
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