Boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space
Optimization and Control
2020-11-30 v1 Analysis of PDEs
Abstract
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing appropriate time-dependent integral transformations in order to map our initial system to a new one which has desired stability properties. The kernels of the integral transformations involved are solutions to non standard multi-dimensional hyperbolic PDEs, where the time dependence introduces several new difficulties in the treatment of their well-posedness. This work generalizes previous results of the literature, where only time-independent systems were considered.
Keywords
Cite
@article{arxiv.2004.12594,
title = {Boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space},
author = {Jean-Michel Coron and Long Hu and Guillaume Olive and Peipei Shang},
journal= {arXiv preprint arXiv:2004.12594},
year = {2020}
}