Perturbations of superstable linear hyperbolic systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| Accesso online: | |
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| _version_ | 1866909951146852352 |
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| author | Kmit, I. Lyul'ko, N. |
| author_facet | Kmit, I. Lyul'ko, N. |
| contents | The paper deals with initial-boundary value problems for linear non-autonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in $L^2$ as well as in $C^1$ under small bounded perturbations. To show this for $C^1$, we prove a general smoothing result implying that the solutions to the perturbed problems become eventually $C^1$-smooth for any $L^2$-initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1605_04703 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Perturbations of superstable linear hyperbolic systems Kmit, I. Lyul'ko, N. Analysis of PDEs 35B20, 35B35, 35B40, 35B45, 35B65, 35L50 The paper deals with initial-boundary value problems for linear non-autonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in $L^2$ as well as in $C^1$ under small bounded perturbations. To show this for $C^1$, we prove a general smoothing result implying that the solutions to the perturbed problems become eventually $C^1$-smooth for any $L^2$-initial data. |
| title | Perturbations of superstable linear hyperbolic systems |
| topic | Analysis of PDEs 35B20, 35B35, 35B40, 35B45, 35B65, 35L50 |
| url | https://arxiv.org/abs/1605.04703 |