Timeline for Asymptotic decay for the wave equation
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Apr 23, 2013 at 10:20 | comment | added | Igor Khavkine | Of course. I intuitively considered $\epsilon$ to be "sufficiently small". | |
| Apr 23, 2013 at 9:19 | comment | added | Willie Wong | For the above analysis you need $\epsilon$ to be sufficiently small compared to the first eigenvalue of the Laplacian. Consider the case $\Omega = [0,\pi]\subset \mathbb{R}$, and $\epsilon = 4$ which is more than twice the first eigenvalue. One checks that $$ y(x,t) = e^{(-2 + \sqrt{3})t} \sin(x)$$ is a solution and decays strictly slower than $e^{-2t}$ ... See en.wikipedia.org/wiki/Damping#Over-damping_.28.CE.B6_.3E_1.29 also for the classical harmonic oscillator analogue. | |
| Apr 23, 2013 at 7:38 | history | answered | Igor Khavkine | CC BY-SA 3.0 |