Differential Equations

Fourier transform restriction phenomena and applications to control of dispersive equations.

Event Date: Oct 10, 2023 in Differential Equations, Seminars

Abstract: In 93′ Jean Bourgain discovered a subtle smoothing property of solutions of the KdV equation posed on a periodic domain. Since this celebrated article, the smoothing properties for dispersive systems are now well known. In this talk, we will see that in the last 15 years, the Bourgain spaces are fundamental to addressing the global control problems in periodic frameworks. Precisely, we will show that the propagation of compactness and regularity have been observed thanks to these spaces in various control problems for dispersive systems.

Variational techniques for non-trivial boundary conditions in fluid dynamics and beyond.

Event Date: Oct 02, 2023 in Differential Equations, Seminars

Abstract: Despite the widely spread usage of no-slip boundary conditions in fluid dynamics, there exist several applications where it is not true that the fluid sticks to the boundary. Instead, the natural condition is setting the normal flux to zero, and then complementing the tangential direction with certain friction conditions known as the Navier boundary condition. In this talk, we will explore the many issues that can arise from strongly imposed boundary conditions in this setting, and how such issues can be alleviated in a way that additionally allows for extreme scale numerical...

Travelling wave solutions to abcd systems.

Event Date: Sep 11, 2023 in Differential Equations, Seminars

Abstract:  We are interested in the so-called abcd system introduced by J. Bona, M. Chen and JC. Saut. Here  we revisit the existence and stability results for travelling waves solutions of these systems.

Event Date: Sep 04, 2023 in Differential Equations, Seminars

Abstract: In this talk, we discuss controllability properties of systems under switching structures. More precisely, we focus on the problem of controlling parabolic systems with several actuators under the constraint that at any given time at most one control is active on the system. We give necessary and sufficient condition, depending only on the underlying operators, for the swtiching controllability to hold.

Prescribing Curvature in Manifolds with Boundary.

Event Date: Aug 28, 2023 in Differential Equations, Seminars

Abstract: In this talk we aim to discuss the problem of finding a Riemannian metric with prescribed curvature in a given compact manifold with nonempty boundary. We are interesting to investigate the problem when the prescribed metric is conformal and also conformally equivalent to some background metric. This is a joint work with Tiarlos Cruz and Feliciano Vitório (UFAL/Brazil).

Algunas soluciones bi y tridimensionales de mapas armónicos inspirados en la biología y la astrofísica.

Event Date: Aug 21, 2023 in Differential Equations, Seminars

Resumen: Presentamos algunas soluciones exactas y aproximadas de mapas armónicos débiles de las ecuaciones  no lineales de Frank-Oseen provenientes de la teoría de cristales líquidos y sus posibles aplicaciones en el marco de la identificación no invasiva de la dirección de fibras musculares en el corazón humano, así como la sorprendente similitud que tienen con ciertas estructuras en en campo de la astrofísica.