Timeline for Are there any physical phenomena of the heat transfer critically depending on diffusion coefficient?
Current License: CC BY-SA 3.0
17 events
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| Aug 14, 2011 at 20:09 | vote | accept | Anand | ||
| Aug 9, 2011 at 4:16 | answer | added | Paul Tupper | timeline score: 4 | |
| Aug 8, 2011 at 21:44 | history | edited | Anand | CC BY-SA 3.0 |
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| Aug 8, 2011 at 21:07 | history | edited | Anand | CC BY-SA 3.0 |
added 303 characters in body; edited title
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| Aug 8, 2011 at 20:37 | comment | added | Anand | Here is a link of Andrew's first reference repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/6061/1/… | |
| Aug 8, 2011 at 20:30 | history | edited | gowers | CC BY-SA 3.0 |
Singular, phenomenon; plural, phenomena.
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| Aug 8, 2011 at 19:46 | comment | added | Andrew | As far as I understand the first was the work of Fujita zentralblatt-math.org/zmath/en/advanced/…. Many others followed. There are numerous works of Pokhozhaev mathnet.ru/php/person.phtml?option_lang=eng&personid=12566. Perhaps references to some recent results could be found there. | |
| Aug 8, 2011 at 19:29 | history | edited | Anand | CC BY-SA 3.0 |
edited title
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| Aug 8, 2011 at 19:27 | comment | added | Anand | @Andrew, thank you very much for the hints. Actually $\sigma$ is Lipschitz continuous which excludes the power function case. Could you give me some references on what you mentioned critical values and subcritical values? Thanks a lot! | |
| Aug 8, 2011 at 19:17 | comment | added | Andrew | @Anand Then it would be nice to write the function $\sigma$. Say if it is а power function, there is a notion of a critical exponent. It depends on dimension. So the value of the exponent what is subcritical for $n=1$ could be critical for $n=2$. | |
| Aug 8, 2011 at 18:53 | history | edited | Anand | CC BY-SA 3.0 |
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| Aug 8, 2011 at 18:52 | comment | added | Anand | @Andrew, my $F(t,x)$ is certain random noise. I am studying the moments of the solution, whose existence depends critically on the value of $\nu$. I forget to say that it is a nonlinear equation. See my edit.:-) | |
| Aug 8, 2011 at 18:49 | comment | added | Michael Kissner | Perhaps, but then we need more Information on $F$ | |
| Aug 8, 2011 at 18:48 | comment | added | Anand | @Michael Kissner, yes, the fundamental solution is dependent on $\nu$ for all dimensions, but without $F$, the solution doesn't depend on $ \nu$ on a critical manner. It is essentially change of the time scale. :-) | |
| Aug 8, 2011 at 18:40 | comment | added | Michael Kissner | Could you elaborate more on the exact problem you are studying? Furthermore, even in $d=1$ the solution depends on $\nu$ (Example: $F=0$, then we have the fundamental solution that is $\nu$-dependent). Not quite sure what you are looking for | |
| Aug 8, 2011 at 18:40 | comment | added | Andrew | Could you elaborate on what properties do you have in mind? Because a dilatation of a space variable $u(x,t)=v(x\nu^{-1/2},t)$ reduces the problem to the case $\nu=1$. So the property you are interested in have to be not invariant under linear transforms. | |
| Aug 8, 2011 at 18:11 | history | asked | Anand | CC BY-SA 3.0 |