Exact Boundary Controllability of Nodal Profile for Nonautonomous Quasilinear Hyperbolic Systems

In this paper, we consider the exact boundary controllability of nodal profile for nonautonomous quasilinear hyperbolic systems on a finite time interval and obtain that there is the exact boundary controllability of nodal profile for any given initial time \(t_0\in \textbf{R}\) $t_0\in \mathbf{R}$ so long as the controllability time \(T>0\) $T>0$ is suitably large, but T depends on \(t_0\) $t_0$ in general. As applications, we discuss the exact boundary controllability of nodal profile for the Saint-Venant system with a nonuniform subcritical steady state and the system of traffic flow depending on time.