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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.05533 |
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| _version_ | 1866918136779898880 |
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| author | Fekirini, Khadidja Louhibi, Naima Benaissa, Abbes |
| author_facet | Fekirini, Khadidja Louhibi, Naima Benaissa, Abbes |
| contents | This paper is devoted to study the well-posedness and stability of degenerate Schrödinger equation with a boundary control acting at the degeneracy. First, we establish the well-posedness of the degenerate problem $v_t(x,t)+\imath(x^αv_x(x,t))_x=0, \hbox{ with } x \in (0,1)$, controlled by Dirichlet-Neumann conditions. Then, exponential and polynomial decreasing of the solution are established. This result is optimal and it is obtained using complex analysis method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of Degenerate Schrödinger Equation with Harmonic Method Fekirini, Khadidja Louhibi, Naima Benaissa, Abbes Analysis of PDEs This paper is devoted to study the well-posedness and stability of degenerate Schrödinger equation with a boundary control acting at the degeneracy. First, we establish the well-posedness of the degenerate problem $v_t(x,t)+\imath(x^αv_x(x,t))_x=0, \hbox{ with } x \in (0,1)$, controlled by Dirichlet-Neumann conditions. Then, exponential and polynomial decreasing of the solution are established. This result is optimal and it is obtained using complex analysis method. |
| title | Stability of Degenerate Schrödinger Equation with Harmonic Method |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.05533 |