Overview

This project is divided into three research axes, all in the field of control theory. The first axis aims at improving a network transport model for viruses spread by mosquitoes such as Zika, Dengue or Chikungunya. The objective is to introduce time-delay terms into the model to take into account delays such as incubation time or reaction time of health authorities. The second axis concerns the controllability of waves in a heterogeneous environment. These media are characterized by discontinuous propagation speed at the interface between two media, leading to refraction phenomena according to Snell’s law. Finally, the last axis aims to study the controllability of nonlinear dispersive equations. These equations can be used to model, for example, the propagation of waves in shallow waters as well as the propagation of signals in an optical fiber.

Keywords

Control theory, linear and nonlinear partial differential equations, epidemiology, waves in heterogeneous media, microlocal analysis, dispersive equations.