Differential Equations

Non-topological condensates for the self-dual Chern-Simons-Higgs model

Event Date: Oct 29, 2013 in Differential Equations, Seminars

Abstract For the abelian self-dual Chern-Simons-Higgs model I will discuss existence issues of periodic vortex configurations — the so-called condensates– of non-topological type for small values of the Chern-Simons parameter k. We provide a positive answer for the existence of non-topological condensates with magnetic field concentrated at some of the vortex points (as a sum of Dirac measures) as k tends to 0. Joint work with M. del Pino, M. Musso and P. Figueroa.

Positive and sign changing solutions to a nonlinear Choquard equation

Event Date: Sep 12, 2013 in Differential Equations, Seminars

Abstract:  (adjunto)

Asymptotics of a reaction-diffusion equation, driven by the fractional Laplacian

Event Date: Aug 14, 2013 in Differential Equations, Seminars

Inspired by some models arising in crystal dislocation, we consider an evolution equation driven by the fractional Laplacian with a small stress that is close to constant in space and time. We show that the solution, in the suitable space and time scale, may be seen as the superposition of a finite number of transition layers. Each transition is centered at a point that evolves by following the external stress and subject to a repulsive potential of fractional type.

Bernstein’s theorem for fractional minimal surfaces

Event Date: Aug 14, 2013 in Differential Equations, Seminars

We discuss a geometric minimization problem arising in a fractional, nonlocal setting. We recall some regularity and rigidity results and we discuss the analogue of Bernstein’s theorem for this kind of minimal surfaces (i.e. whether minimal graphs are necessarily affine).

Superficies Mínimas no locales

Event Date: Mar 25, 2013 in Differential Equations, Seminars

Rapid convergence to quasi-stationary states for the 2D Navier-Stokes equation

Event Date: Mar 14, 2012 in Differential Equations, Seminars