Differential Equations

Existence and stability of steady states of Flat Vlasov Poisson with a central mass density.

Event Date: Nov 15, 2022 in Differential Equations, Seminars

Abstract: El Sistema de Vlasov-Poisson Plano es usado para modelar objetos astronómicos extremadamente planos, a través de la evolución de una distribución de partículas en el plano de fase, las cuales autointeractúan a través del campo gravitacional inducido por ellas mismas. En este trabajo se estudia la construcción de estados estacionarios del Sistema de Vlasov-Poisson Plano en presencia de un potencial gravitacional externo, inducido por una densidad de masa fija. La construcción de dichos estados se realiza a través de la minimización de los funcionales de Energía-Casimir, los cuales...

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Recent developments in Fourier interpolation theory.

Event Date: Nov 08, 2022 in Differential Equations, Seminars

Abstract: In this talk we will discuss some problems related to the notion of Fourier interpolation:  formulas where one can recover functions from its values over a certain discrete set, and the values of its Fourier transform over a dual discrete set. These formulas arrive naturally in many situations, and we will mention a few related to certain kinds of uncertainty principles, and the theory of sphere packing.  

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Qualitative Properties for a class of fully nonlinear elliptic equations.

Event Date: Oct 27, 2022 in Differential Equations, Seminars

Abstract: In joint work with F. Pacella, we study the existence and asymptotic behavior of radial positive solutions of some fully nonlinear equations involving Pucci’s extremal operators in dimension two and higher. In particular we prove the existence of a positive solution of a fully nonlinear version of the Liouville equation in the plane. Moreover, for the (negative) Pucci P^- operator, we show the existence of a critical exponent and give bounds for it. The same technique is then applied in higher dimensions to improve the previously known bounds  

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Existence and multiplicity of positive solutions to the scalar-field equation on large annuli in the three-dimensional sphere.

Event Date: Oct 25, 2022 in Differential Equations, Seminars

Abstract: In this talk, we consider the Dirichlet problem for the scalar-field equation in a large annulus in the three-dimensional sphere. We obtain the existence, uniqueness, and multiplicity results of the positive solutions depending only on the latitude. This is joint work with Noaki Shioji (Yokohama National University) and Kohtaro Watanabe (National Defense Academy).

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Ecuaciones integro-diferenciales y procesos semi-markovianos.

Event Date: Oct 18, 2022 in Differential Equations, Seminars

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.

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Inverse scattering for critical semilinear wave equations.

Event Date: Oct 06, 2022 in Differential Equations, Seminars

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.

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