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

2 CaGE - Control And GEometry
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
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.
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Journal articles

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https://hal.archives-ouvertes.fr/hal-02553027
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Submitted on : Friday, April 24, 2020 - 9:07:21 AM
Last modification on : Friday, August 19, 2022 - 9:18:40 AM

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### Citation

Jean-Michel Coron, Long Hu, Guillaume Olive, Peipei Shang. Boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. Journal of Differential Equations, 2021, 271, pp.1109-1170. ⟨10.1016/j.jde.2020.09.037⟩. ⟨hal-02553027⟩

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