Finite Time Stabilization of Nonautonomous First Order Hyperbolic Systems

Irina Kmit; Natalya Lyul'ko

doi:10.1137/20m1343610

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arXiv · 2006.05105

Finite Time Stabilization of Nonautonomous First Order Hyperbolic Systems

Irina Kmit·Natalya Lyul'ko

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Abstract

We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions ensuring that solutions stabilize to zero in a finite time for any initial $L^2$-data. In the nonautonomous case we give a combinatorial criterion stating that the robust stabilization occurs if and only if the matrix of reflection boundary coefficients corresponds to a directed acyclic graph. An equivalent robust algebraic criterion is that the adjacency matrix of this graph is nilpotent. In the autonomous case we also provide a spectral stabilization criterion, which is nonrobust with respect to perturbations of the coefficients of the hyperbolic system.

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BibTeX RIS

Irina Kmit, Natalya Lyul'ko. 2020-06-09. Finite Time Stabilization of Nonautonomous First Order Hyperbolic Systems. https://doi.org/10.1137/20m1343610

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