Timeline for Iterated integrations by parts using the fractional Laplacian
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 13, 2021 at 18:45 | vote | accept | Riku | ||
| Nov 6, 2021 at 16:49 | comment | added | Mateusz Kwaśnicki | I would have tried some energy conservation laws, but I never worked with the wave equation really. There are some recent works on this subject, e.g. DOI:10.1515/fca-2018-0067. | |
| Nov 6, 2021 at 13:18 | comment | added | Riku | Ok, I see. Then my real question is the following one: without this trick, how can we prove that $$U(t,x) = \sum_{k=1}^\infty \varphi_k(x) \left( \langle u, \varphi_k \rangle \frac{\sin(\sqrt{\lambda_k} t)}{\sqrt{\lambda_k}} \right)$$ (which is the solution of the fractional wave equation in a regular open set $\Omega$ with initial velocity $u$ and zero initial displacement) is smooth in $x \in \Omega$ if $u$ is smooth? | |
| Nov 6, 2021 at 11:08 | history | answered | Mateusz Kwaśnicki | CC BY-SA 4.0 |