Finite Time Stabilization of Nonautonomous First Order Hyperbolic Systems
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915662659584000 |
|---|---|
| author | Kmit, Irina Lyul'ko, Natalya |
| author_facet | Kmit, Irina Lyul'ko, Natalya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_05105 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Finite Time Stabilization of Nonautonomous First Order Hyperbolic Systems Kmit, Irina Lyul'ko, Natalya Analysis of PDEs 35B40, 93D20, 93D40, 35L04, 37L15 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. |
| title | Finite Time Stabilization of Nonautonomous First Order Hyperbolic Systems |
| topic | Analysis of PDEs 35B40, 93D20, 93D40, 35L04, 37L15 |
| url | https://arxiv.org/abs/2006.05105 |