Project MATH-AMSUD-ANID 21-MATH-03
January 2021 - December 2021
Roberto De Almeida [P], Marcelo Cavalcanti, David Dos Santos Ferreira, Jose Raul Quintero, Mauricio Sepúlveda:
Control Theory and Microlocal Analysis with Applications in Partial Differential Equations
We aim to the analysis of diverse aspects in the study of dispersive equations under the scrutiny of microlocal analysis and other techniques, including some applications. As some partial differential equations appearing in models for several physical phenomena, we plan to study well-posedness, control and stabilization properties for Benney-Luke, Boussinesq KdV-KdV type systems which describes the propagation of bidirectional water waves, for Schrödinger on exterior domains which is a model of wave propagation in fiber optics and for biharmonic Schrödinger equation (or fourth order Schrödinger equation) on different domains which physically represents the propagation of intense laser beams.