Timeline for Solution to Heat Equation By Projection
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2019 at 13:01 | comment | added | ABIM | Fair enough, then I will restrict the supremum to a compact set. This takes care of the problem. | |
| Nov 28, 2019 at 13:01 | history | edited | ABIM | CC BY-SA 4.0 |
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| Nov 27, 2019 at 12:55 | review | Close votes | |||
| Dec 2, 2019 at 3:05 | |||||
| Nov 27, 2019 at 12:46 | comment | added | Mateusz Kwaśnicki | @N00ber: Your edit changes nothing: every "unusual" solution will grow even faster. See this article by Tychonoff, and this answer by George Lowther. | |
| Nov 27, 2019 at 10:54 | comment | added | ABIM | We can assume that $p$ has finite sup and that it is strictly non-negatively valued. | |
| Nov 27, 2019 at 10:53 | history | edited | ABIM | CC BY-SA 4.0 |
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| Nov 26, 2019 at 17:59 | comment | added | Christian Remling | The fact that $p$ is completely arbitrary as a function of $t$ seems a strange feature of the set-up. For example, for many $p$'s the supremum will just be infinite for any $u$. | |
| Nov 26, 2019 at 15:59 | comment | added | Dirk | If you want to project, you should minimize instead of maximize, right? To clarify: $p(t,x)$ is given and you want to find $u\in X$ which minimizes the distance $\|u-p\|$? (Which norm, by the way…) | |
| Nov 26, 2019 at 12:38 | comment | added | Mateusz Kwaśnicki | I mean: if $u_1$ and $u_2$ are solutions and both $u_1-p$ and $u_2-p$ are bounded, then $u_1-u_2$ is a bounded solution with zero initial data, and hence $u_1=u_2$. | |
| Nov 26, 2019 at 12:36 | comment | added | ABIM | But p does not solve the heat equation so the difference $u-p$ is not a solution to the heat equatoin, in general. | |
| Nov 26, 2019 at 10:56 | comment | added | Mateusz Kwaśnicki | If there is any such solution, it is automatically a minimizer. Indeed: the difference of any two solutions is a solution of the heat equation with zero initial data, and hence it is either unbounded or identically zero. | |
| Nov 26, 2019 at 10:42 | history | asked | ABIM | CC BY-SA 4.0 |