Timeline for Decay estimate for the heat equation: $\sup_{t>0}\int_{\mathbb{R}} t^\alpha |u_x|^2\ dx$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20, 2019 at 14:47 | vote | accept | Riku | ||
| Oct 12, 2018 at 18:37 | answer | added | Cesar J. Niche | timeline score: 4 | |
| S Aug 6, 2018 at 19:02 | history | bounty ended | CommunityBot | ||
| S Aug 6, 2018 at 19:02 | history | notice removed | CommunityBot | ||
| Jul 30, 2018 at 19:38 | comment | added | Jochen Glueck | I posted the details in an answer (and it seems that there was a small computational error in the constant in front of the integral in my above comment). | |
| Jul 30, 2018 at 19:36 | answer | added | Jochen Glueck | timeline score: 3 | |
| Jul 30, 2018 at 10:26 | answer | added | Denis Serre | timeline score: 4 | |
| Jul 29, 2018 at 19:10 | comment | added | Riku | @JochenGlueck Yes, please, I'd like to know the details. Especially about the meaning of that integral. | |
| Jul 29, 2018 at 18:35 | comment | added | Jochen Glueck | Using the Fourier transform with respect to the spatial variable it is not difficult to show the (possibly non-optimal) estimate $\sup_{t > 0} \int_{\mathbb{R}} t^\alpha \lvert u_x\rvert^2 dx \le (\alpha/e)^\alpha \int_{\mathbb{R}} \lvert x\rvert^{2-2\alpha} \lvert \hat u_0(x)\rvert^2 dx$; for $\alpha \in (0,1)$ the integral on the right is closely related to a Sobolev norm of $u_0$. If this is of any help for you I can post the details. | |
| S Jul 29, 2018 at 17:17 | history | bounty started | Riku | ||
| S Jul 29, 2018 at 17:17 | history | notice added | Riku | Authoritative reference needed | |
| Jul 26, 2018 at 19:42 | history | asked | Riku | CC BY-SA 4.0 |