Timeline for Finite speed of propagation of wave equation
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2014 at 15:50 | comment | added | Willie Wong | I am more wondering about the reverse: how bad must the interior be if the boundary is a fractal. And to your reply, no, not quite: for the Sierpinski gasket, for the purpose of its Laplacian, the boundary is only the three vertices of the big triangle. So the boundary is not a fractal. (Note that this boundary is not a boundary in the topological sense, but is the sense for which the boundary value problem makes sense; this has to do with how the fractal Laplacian is defined.) | |
| Jun 19, 2014 at 14:46 | comment | added | Carlo Beenakker | hmm, I didn't intend to make a subtle distinction here, but if a fractal, say the Sierpinski gasket, is embedded in three-dimensional space, doesn't its boundary have a fractal dimension? | |
| Jun 19, 2014 at 14:32 | comment | added | Willie Wong | from best I can tell the links you gave says infinite propagation speed is possible for wave equations on fractals, not wave equations on sets whose boundaries are fractals. | |
| Jun 19, 2014 at 13:27 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |