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Tuesday Seminar of Analysis
Seminar information archive ～05/08｜Next seminar｜Future seminars 05/09～
| Date, time & place | Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi |
2024/12/24
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
KAKEHI Tomoyuki (University of Tsukuba)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
https://forms.gle/2otzqXYVD6DqM11S8
KAKEHI Tomoyuki (University of Tsukuba)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
[ Abstract ]
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 ∂2tu−Δu=0 on Rn with the condition u|t=t1=f1,⋯,u|t=tm=fm. 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 {f1,⋯,fm} the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that m=3 and (t3−t1)/(t2−t1) is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data {f1,f2,f3}. 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.
[ Reference 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 ∂2tu−Δu=0 on Rn with the condition u|t=t1=f1,⋯,u|t=tm=fm. 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 {f1,⋯,fm} the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that m=3 and (t3−t1)/(t2−t1) is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data {f1,f2,f3}. 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
