Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866913146158972928 |
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| author | Yang, Dong-Hui Guo, Bao-Zhu |
| author_facet | Yang, Dong-Hui Guo, Bao-Zhu |
| contents | In this study, we firstly establish the well-posedness of a degenerate parabolic equation under Dirichlet boundary conditions. Following this, we introduce a shape design problem, which acts as a framework for approximating the degenerate parabolic equation through a series of uniformly parabolic equations. Finally, as a tangible application of this shape design approach, we deduce a boundary observability inequality associated with the degenerate parabolic equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19599 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability Yang, Dong-Hui Guo, Bao-Zhu Analysis of PDEs Optimization and Control In this study, we firstly establish the well-posedness of a degenerate parabolic equation under Dirichlet boundary conditions. Following this, we introduce a shape design problem, which acts as a framework for approximating the degenerate parabolic equation through a series of uniformly parabolic equations. Finally, as a tangible application of this shape design approach, we deduce a boundary observability inequality associated with the degenerate parabolic equation. |
| title | Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2605.19599 |