Timeline for an inverse problem related to gaussian integral
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 26, 2016 at 13:27 | comment | added | Andrew | @jian Uniqueness holds according to Terry Tao's comment mathoverflow.net/questions/72195/… | |
| Feb 25, 2016 at 0:35 | comment | added | reuns | you can recover $\rho(x,t)$ iff you can reconstruct $(\rho \ast K)(x,t)$ for every $x,t$. so you'll need more than $f_T(.)$ for a single $T$, for example you'll need $\displaystyle\frac{\partial^k f}{\partial T^k}(x,T)$ for every $k,x$ | |
| Feb 24, 2016 at 14:07 | history | edited | jian | CC BY-SA 3.0 |
deleted 15 characters in body
|
| Feb 23, 2016 at 12:56 | comment | added | Christian Clason | I second Dirk's suggestion -- if the heat equation is one-dimensional, Cannon's book has more about it than you've ever wanted to know. From my experience, determining space- and time-dependent $\rho$ could be tricky; you'd have much better chance if you have $\rho=\rho_1(t)\rho_2(x)$, where one of the two factors is known. | |
| Feb 23, 2016 at 11:45 | history | edited | jian | CC BY-SA 3.0 |
edited body
|
| Feb 23, 2016 at 10:22 | comment | added | Dirk | @yimin Sounds strange at first sight, that this may well be possible (note that $f_T(x)$ can be an analytic function in $x$ and $T$ and hence, determined if known on a set with some cluster point). More to the OP: I don't know the answer but I vaguely remember that the book The One-Dimensional Heat Equation by Cannon is a great source for such questions. | |
| Feb 23, 2016 at 3:53 | comment | added | Yimin | sounds like recovering a 2d function from 1d measurement? | |
| Feb 23, 2016 at 3:38 | history | edited | jian | CC BY-SA 3.0 |
edited body
|
| Feb 22, 2016 at 12:12 | history | asked | jian | CC BY-SA 3.0 |