Solving the Scattering Problem for Open Wave-Guide Networks, II Outgoing Estimates
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914144599408640 |
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| author | Epstein, Charles L. |
| author_facet | Epstein, Charles L. |
| contents | The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution of the physical problem to a transmission problem rephrased as a system of integral equations on the common perpendicular line. In this part we show that solutions of the integral equations introduced in Part I have asymptotic expansions, if the data allows it. Using these expansions we show that the solutions to the PDE found in each half space satisfy appropriate outgoing radiation conditions. In Part III we show that these conditions imply uniqueness of the solution to the PDE as well as uniqueness for our system of integral equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05816 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solving the Scattering Problem for Open Wave-Guide Networks, II Outgoing Estimates Epstein, Charles L. Mathematical Physics Numerical Analysis Analysis of PDEs 35C15, 35Q60, 65M80, 65R20 The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution of the physical problem to a transmission problem rephrased as a system of integral equations on the common perpendicular line. In this part we show that solutions of the integral equations introduced in Part I have asymptotic expansions, if the data allows it. Using these expansions we show that the solutions to the PDE found in each half space satisfy appropriate outgoing radiation conditions. In Part III we show that these conditions imply uniqueness of the solution to the PDE as well as uniqueness for our system of integral equations. |
| title | Solving the Scattering Problem for Open Wave-Guide Networks, II Outgoing Estimates |
| topic | Mathematical Physics Numerical Analysis Analysis of PDEs 35C15, 35Q60, 65M80, 65R20 |
| url | https://arxiv.org/abs/2310.05816 |