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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1604.04401 |
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| _version_ | 1866918239244648448 |
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| author | Kmit, I. Klyuchnyk, R. |
| author_facet | Kmit, I. Klyuchnyk, R. |
| contents | We investigate a large class of linear boundary value problems for the general first-order one-dimensional hyperbolic systems in the strip $[0,1]\times\R$. We state rather broad natural conditions on the data under which the operators of the problems satisfy the Fredholm alternative in the spaces of continuous and time-periodic functions. A crucial ingredient of our analysis is a non-resonance condition, which is formulated in terms of the data responsible for the bijective part of the Fredholm operator. In the case of $2\times 2$ systems with reflection boundary conditions, we provide a criterium for the non-resonant behavior of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1604_04401 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Fredholm Solvability of Time-Periodic Boundary Value Hyperbolic Problems Kmit, I. Klyuchnyk, R. Analysis of PDEs We investigate a large class of linear boundary value problems for the general first-order one-dimensional hyperbolic systems in the strip $[0,1]\times\R$. We state rather broad natural conditions on the data under which the operators of the problems satisfy the Fredholm alternative in the spaces of continuous and time-periodic functions. A crucial ingredient of our analysis is a non-resonance condition, which is formulated in terms of the data responsible for the bijective part of the Fredholm operator. In the case of $2\times 2$ systems with reflection boundary conditions, we provide a criterium for the non-resonant behavior of the system. |
| title | Fredholm Solvability of Time-Periodic Boundary Value Hyperbolic Problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1604.04401 |