Well-posedness for the biharmonic scattering problem for a penetrable obstacle
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arXiv
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| Format: | Preprint |
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2025
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| author | Ayala, Rafael Ceja Harris, Isaac Sánchez-Vizuet, Tonatiuh |
| author_facet | Ayala, Rafael Ceja Harris, Isaac Sánchez-Vizuet, Tonatiuh |
| contents | We address the direct scattering problem for a penetrable obstacle in an infinite elastic two--dimensional Kirchhoff--Love plate. Under the assumption that the plate's thickness is small relative to the wavelength of the incident wave, the propagation of perturbations on the plate is governed by the two-dimensional biharmonic wave equation, which we study in the frequency domain. With the help of an operator factorization, the scattering problem is analyzed from the perspective of a coupled boundary value problem involving the Helmholtz and modified Helmholtz equations. Well-posedness and reciprocity relations for the problem are established. Numerical examples for some special cases are provided to validate the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness for the biharmonic scattering problem for a penetrable obstacle Ayala, Rafael Ceja Harris, Isaac Sánchez-Vizuet, Tonatiuh Analysis of PDEs 47A40, 74J05, 74H25, 35J35 We address the direct scattering problem for a penetrable obstacle in an infinite elastic two--dimensional Kirchhoff--Love plate. Under the assumption that the plate's thickness is small relative to the wavelength of the incident wave, the propagation of perturbations on the plate is governed by the two-dimensional biharmonic wave equation, which we study in the frequency domain. With the help of an operator factorization, the scattering problem is analyzed from the perspective of a coupled boundary value problem involving the Helmholtz and modified Helmholtz equations. Well-posedness and reciprocity relations for the problem are established. Numerical examples for some special cases are provided to validate the theoretical findings. |
| title | Well-posedness for the biharmonic scattering problem for a penetrable obstacle |
| topic | Analysis of PDEs 47A40, 74J05, 74H25, 35J35 |
| url | https://arxiv.org/abs/2506.10176 |