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

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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Submitted on : Friday, April 24, 2020 - 9:07:21 AM
Last modification on : Wednesday, June 2, 2021 - 4:26:58 PM

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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, Elsevier, 2021, 271, pp.1109-1170. ⟨10.1016/j.jde.2020.09.037⟩. ⟨hal-02553027⟩

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