Timeline for What happens to the boundary conditions as a PDE is approximated by a lesser order PDE?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Sep 26, 2012 at 8:04 | vote | accept | Ryan Thorngren | ||
| Aug 21, 2010 at 1:17 | answer | added | Aleksey Pichugin | timeline score: 3 | |
| Jul 25, 2010 at 23:29 | comment | added | Willie Wong | also, does it even make sense to think of the limit? Since the derivative is generally an unbounded operator, I don't see how the limit can be justified to exist. (In other words, $\epsilon\nabla^4 u$ can still be potentially be much larger than $\nabla^2 u$ for arbitrarily small $\epsilon$, so one cannot really say that one can get an approximation by removing the term containing the "smallness parameter".) | |
| Jul 24, 2010 at 8:10 | comment | added | Harald Hanche-Olsen | Wouldn't it be more appropriate to consider the limit of $\epsilon\nabla^4u+\nabla^2u-\lambda u=F(x,y)$ as $\epsilon\to0$? The way you write it, as $c\to\infty$ I would expect to be left with just $\nabla^2\tilde u=0$. | |
| Jul 23, 2010 at 19:00 | history | asked | Ryan Thorngren | CC BY-SA 2.5 |