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 t0∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_0\in \textbf{R}$$\end{document} so long as the controllability time T>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T>0$$\end{document} is suitably large, but T depends on t0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_0$$\end{document} 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.