Sharp dispersive estimates for the wave equation on the 5-dimensional lattice graph
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929371051196416 |
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| author | Bi, Cheng Cheng, Jiawei Hua, Bobo |
| author_facet | Bi, Cheng Cheng, Jiawei Hua, Bobo |
| contents | Schultz \cite{S98} proved dispersive estimates for the wave equation on lattice graphs $\mathbb{Z}^d$ for $d=2,3,$ which was extended to $d=4$ in \cite{BCH23}. By Newton polyhedra and the algorithm introduced by Karpushkin \cite{K83}, we further extend the result to $d=5:$ the sharp decay rate of the fundamental solution of the wave equation on $\mathbb{Z}^5$ is $|t|^{-\frac{11}{6}}.$ Moreover, we prove Strichartz estimates and give applications to nonlinear equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp dispersive estimates for the wave equation on the 5-dimensional lattice graph Bi, Cheng Cheng, Jiawei Hua, Bobo Analysis of PDEs Schultz \cite{S98} proved dispersive estimates for the wave equation on lattice graphs $\mathbb{Z}^d$ for $d=2,3,$ which was extended to $d=4$ in \cite{BCH23}. By Newton polyhedra and the algorithm introduced by Karpushkin \cite{K83}, we further extend the result to $d=5:$ the sharp decay rate of the fundamental solution of the wave equation on $\mathbb{Z}^5$ is $|t|^{-\frac{11}{6}}.$ Moreover, we prove Strichartz estimates and give applications to nonlinear equations. |
| title | Sharp dispersive estimates for the wave equation on the 5-dimensional lattice graph |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.00949 |