Monday October, 24, 2016
Sala de seminarios del 5to. piso del DIM, U. de Chile.
Nicola Abatangelo (U. Libre Bruselas)
Title: Loss of maximum principles for higher-order fractional Laplacians
It is long since known that the bilaplacian operator (namely, the square of the Laplacian), when coupled with Dirichlet boundary conditions, does not satisfy a maximum principle in general. We investigate whether maximum principles do hold or not for powers of the Laplacian between 1 and 2, and for other positive powers. We will show how the property is lost in general on disconnected domains, but it is still preserved on spherical ones. This is a joint work with S. Jarohs (Frankfurt) and A. Saldana (Lisbon).
Márcio Cavalcante (CMM)
Title: The initial-boundary value problem for the Schrödinger-Korteweg-de Vries system on the half-line
We present some local well-posedness results for the initial-boundary value problem (IBVP) associated to the Schrödinger-Korteweg de Vries system on right and left half-lines. The results are obtained in the low regularity setting by using two analytic families of boundary forcing operators, one of these was developed by Holmer for the IBVP associated to the Korteweg-de Vries equation (Communications in Partial Differential Equations, 31 (2006)) and the other one was recently introduced by myself in the context of nonlinear Schrödinger with quadratic nonlinearities. This is a joint work with A.J. Corcho.
Next Seminar: Monday, Noviembre 7, 2016.