Pattern formations of coupled PDEs with transparent boundary conditions in product-type ends and applications
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866908457036152832 |
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| author | Diao, Huaian Liu, Hongyu Meng, Qingle Wang, Li |
| author_facet | Diao, Huaian Liu, Hongyu Meng, Qingle Wang, Li |
| contents | This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement), spectral geometry of transmission eigenfunctions, and geometric characterization of invisibility phenomena and inverse shape problems in wave scattering. We uncover and rigorously characterize a novel local pattern formation, establishing a sharp quantitative relationship between the difference in the PDEs' lower-order terms and the geometric/regularity parameters within a generic domain's product-type ends-structures characterized by high extrinsic curvature. This foundational result yields new findings with novel physical insights and practical implications across these fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pattern formations of coupled PDEs with transparent boundary conditions in product-type ends and applications Diao, Huaian Liu, Hongyu Meng, Qingle Wang, Li Analysis of PDEs This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement), spectral geometry of transmission eigenfunctions, and geometric characterization of invisibility phenomena and inverse shape problems in wave scattering. We uncover and rigorously characterize a novel local pattern formation, establishing a sharp quantitative relationship between the difference in the PDEs' lower-order terms and the geometric/regularity parameters within a generic domain's product-type ends-structures characterized by high extrinsic curvature. This foundational result yields new findings with novel physical insights and practical implications across these fields. |
| title | Pattern formations of coupled PDEs with transparent boundary conditions in product-type ends and applications |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.14779 |