Exponential stability of solutions to perturbed superstable wave equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866908700388622336 |
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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 the linear wave equation 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 $C^2$ under small bounded perturbations of the wave operator. To show this for $C^2$, we prove a smoothing result implying that the solutions to the perturbed problems become eventually $C^2$-smooth for any $H^1\times L^2$-initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_02856 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Exponential stability of solutions to perturbed superstable wave equations Kmit, I. Lyul'ko, N. Analysis of PDEs 35B20, 35B35, 35B40, 35B45, 35B65, 35L50 The paper deals with initial-boundary value problems for the linear wave equation 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 $C^2$ under small bounded perturbations of the wave operator. To show this for $C^2$, we prove a smoothing result implying that the solutions to the perturbed problems become eventually $C^2$-smooth for any $H^1\times L^2$-initial data. |
| title | Exponential stability of solutions to perturbed superstable wave equations |
| topic | Analysis of PDEs 35B20, 35B35, 35B40, 35B45, 35B65, 35L50 |
| url | https://arxiv.org/abs/1801.02856 |