Special Session 99: Emerging Trends in Analysis and Control of PDEs

A method to determine the minimal null control time of one-dimensional linear hyperbolic systems
Guillaume Olive
Jagiellonian University
Poland
Co-Author(s):    
Abstract:
In this talk, we address the problem of null controllability for one-dimensional first-order linear hyperbolic systems of the form: $$ \begin{cases} \frac{\partial y}{\partial t}(t,x)+\Lambda(x) \frac{\partial y}{\partial x}(t,x)=M(x) y(t,x), \ y_-(t,1)=u(t), \quad y_+(t,0)=Qy_-(t,0), \ y(0,x)=y^0(x), \end{cases} \quad (t,x) \in (0,T) \times (0,1), $$ where $u:(0,T) \to \mathbb{R}^m$ is the control. We present a method to find the minimal control time when the coefficients are regular enough. This presentation is based on a joint work with Long Hu (https://doi.org/10.1016/j.jde.2025.113455)