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解析学火曜セミナー
過去の記録 ～12/07｜次回の予定｜今後の予定 12/08～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 156号室 |
|---|---|
| 担当者 | 石毛 和弘, 坂井 秀隆, 伊藤 健一 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/analysis/ |
2024年12月24日(火)
16:00-17:30 数理科学研究科棟(駒場) 128号室
対面・オンラインハイブリッド開催，場所にご注意ください
筧知之 氏 (筑波大学)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
https://forms.gle/2otzqXYVD6DqM11S8
対面・オンラインハイブリッド開催，場所にご注意ください
筧知之 氏 (筑波大学)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
[ 講演概要 ]
In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution.
We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
[ 参考URL ]In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution.
We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
https://forms.gle/2otzqXYVD6DqM11S8
