Nonlinear stability in seismic waves

Adham A. Ali, Dmitry Strunin

Abstract


We analyse a passive system featuring a neutrally stable short-wavelength mode. The system is modelled by the Nikolaevskiy equation relevant to elastic waves, reaction-diffusion systems and convection. After quickly falling onto a centre manifold, the system then exhibits slow decay. Using the centre manifold technique, we deduce that the decay law is the inverse square root of time. The result is confirmed by direct computations of the system.

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DOI: http://dx.doi.org/10.21914/anziamj.v57i0.10441



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.