Fredholm Solvability of Periodic Neumann Problem for a Linear Telegraph Equation
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arXiv
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| Format: | Preprint |
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2011
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| _version_ | 1866911309639974912 |
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| author | Kmit, Irina |
| author_facet | Kmit, Irina |
| contents | We investigate the linear telegraph equation $$ u_{tt}-u_{xx}+2μu_t=f(x,t) $$ with periodic Neumann boundary conditions. We prove that the operator of the problem is modeled as a Fredholm operator of index zero in the scale of Sobolev-type spaces of periodic functions. This result extends to small perturbations of the equation where $μ$ becomes variable and discontinuous or an additional zero-order term appears. We also show that the solutions to the problem are smoothing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1106_1517 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Fredholm Solvability of Periodic Neumann Problem for a Linear Telegraph Equation Kmit, Irina Analysis of PDEs 35L20, 35B10 We investigate the linear telegraph equation $$ u_{tt}-u_{xx}+2μu_t=f(x,t) $$ with periodic Neumann boundary conditions. We prove that the operator of the problem is modeled as a Fredholm operator of index zero in the scale of Sobolev-type spaces of periodic functions. This result extends to small perturbations of the equation where $μ$ becomes variable and discontinuous or an additional zero-order term appears. We also show that the solutions to the problem are smoothing. |
| title | Fredholm Solvability of Periodic Neumann Problem for a Linear Telegraph Equation |
| topic | Analysis of PDEs 35L20, 35B10 |
| url | https://arxiv.org/abs/1106.1517 |