Timeline for Physical interpretation of Robin boundary conditions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 27, 2022 at 11:46 | comment | added | Manuel Pena | That infinity condition is like Sommerfeld's radiation condition for the Helmholtz equation, which arises studying two-dimensional standing waves in electromagnetism | |
| May 4, 2012 at 13:39 | comment | added | Yakov Shlapentokh-Rothman | I'm not really sure what this says about "why" there is dispersion, but I'm really the wrong person to ask. One nice thing about this approach is that it generalizes to Riemannian manifolds with a potential naturally, i.e. you can end up reducing certain dispersive statements about the wave equation to some geometric assumptions about the manifold (like behavior of trapped geodesics and asymptotic flastness) and/or spectral assumptions about $\Delta_g + V$. From what I can tell, there is a large literature on this. A more recent paper is arxiv.org/abs/1105.0873. See Proposition 1.38. | |
| May 3, 2012 at 1:29 | comment | added | Otis Chodosh | Thanks! I didnt know about this. Does this sort of say that high energy/frequency waves have to die out at infinity because we expect that Robin -> Dirichlet as $\omega \to \infty$? | |
| May 3, 2012 at 1:23 | vote | accept | Otis Chodosh | ||
| Apr 30, 2012 at 17:08 | history | answered | Yakov Shlapentokh-Rothman | CC BY-SA 3.0 |