Timeline for How fast does the Heat equation with boundary condition $\frac{\partial u}{\partial \vec{n}}=u^2$ decay?
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| Feb 14, 2014 at 3:25 | comment | added | Fantastic | I think the calculations are correct, though It does NOT tell us the decay rate. Now we have $$\|u(t)\|^2\leq C\,\exp^{-\lambda \int_0^tm(s)ds}$$ Unless we know a lower bound for $m(t)$, it is as hard as the original question. Thanks for the elegant calculation though. | |
| Feb 13, 2014 at 23:29 | history | edited | SetHead | CC BY-SA 3.0 |
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| Feb 13, 2014 at 21:04 | history | undeleted | SetHead | ||
| Feb 13, 2014 at 21:03 | history | edited | SetHead | CC BY-SA 3.0 |
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| Feb 13, 2014 at 20:12 | history | deleted | SetHead | via Vote | |
| Feb 13, 2014 at 20:10 | review | First posts | |||
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| Feb 13, 2014 at 20:03 | comment | added | Michael Renardy | He specified that n is the inward normal, so you have the opposite sign. That is, the heat flux is outward, and one should expect decay rather than blowup. | |
| Feb 13, 2014 at 19:54 | history | answered | SetHead | CC BY-SA 3.0 |