Exact boundary observability for nonautonomous quasilinear wave equations

By means of a direct and constructive method based on the theory of semiglobal $C^2$ solution, the local exact boundary observability is shown for nonautonomous 1-D quasilinear wave equations. The essential difference between nonautonomous wave equations and autonomous ones is also revealed.Comment: 18 pages, 5 figure

Lyapunov functions and finite time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems

Hyperbolic systems in one dimensional space are frequently used in modeling of many physical systems. In our recent works, we introduced time independent feedbacks leading to the finite stabilization for the optimal time of homogeneous linear and quasilinear hyperbolic systems. In this work, we present Lyapunov's functions for these feedbacks and use estimates for Lyapunov's functions to rediscover the finite stabilization results.Comment: arXiv admin note: text overlap with arXiv:2005.1326

Null controllability and finite-time stabilization in minimal time of one-dimensional first-order 2 × 2 linear hyperbolic systems

The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order 2 ×2 linear hyperbolic systems. The main technical point is to show that we cannot obtain a better time. The proof combines the backstepping method with the Titchmarsh convolution theorem