Young Researchers Workshop: Ki-Net 2012-2019

Stabilization of 1-D hyperbolic systems on a bounded domain.

Amaury Hayat

Ecole des Ponts Paristech / Rutgers University

Hyperbolic systems are largely widespread in physics and industrial applications for their ability to model transport phenomena. To understand the physical behaviors associated or to design practical applications, it is necessary to study the stability or stabilizability of their steady-states. In this talk we will study the stability and stabilization of 1-D hyperbolic systems when we can act at the boundaries. The steady-states considered may be non-uniform or may include a discontinuity, which give rise to many interesting phenomena, such as an intrinsic limit length of stability. We will start with general abstract results and then move to particular physical systems. In particular, we will show the existence of a local entropy that enables the stabilization of any physical density-velocity systems, even when most of the physical data associated are unknown (pressure model, friction model, slope, etc.).