# Boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space

arXiv: https://arxiv.org/abs/2004.12594 · HTML: https://mlsanity.com/paper/2004.12594/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2020.

## Built on by (most cited first, 1 of 1)

- [Backstepping Neural Operators for 2× 2 Hyperbolic PDEs](https://mlsanity.com/paper/2312.16762/) (2023)

## Abstract (arXiv)

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.