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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.10592 |
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| _version_ | 1866911919132114944 |
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| author | Bies, Piotr Michał |
| author_facet | Bies, Piotr Michał |
| contents | We consider conditions for the decay in time of solutions of non-homogenous hyperbolic equations. It is proven that solutions of the equations go to $0$ in $L^2$ at infinity if and only if an equation's right-hand side uniquely determines the initial conditions in a certain way. We also obtain that a hyperbolic equation has a unique solution that fades when $t\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10592 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decay of solutions of non-homogenous hyperbolic equations Bies, Piotr Michał Analysis of PDEs We consider conditions for the decay in time of solutions of non-homogenous hyperbolic equations. It is proven that solutions of the equations go to $0$ in $L^2$ at infinity if and only if an equation's right-hand side uniquely determines the initial conditions in a certain way. We also obtain that a hyperbolic equation has a unique solution that fades when $t\to\infty$. |
| title | Decay of solutions of non-homogenous hyperbolic equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.10592 |