Nonlinear stability in seismic waves

Ali, Adham A. and Strunin, Dmitry V. (2017) Nonlinear stability in seismic waves. Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 57. C382-C397. ISSN 1445-8735

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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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Article published in 2017, in the vol. 57 2015 issue of The ANZIAM Journal. Published version embargoed until 1 January 2020 (2 years), in accordance with the copyright policy of the publisher. Published as part of the Proceedings of the 12th Biennial Engineering Mathematics and Applications Conference.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 11 Jun 2019 00:29
Last Modified: 18 Jun 2019 04:16
Fields of Research : 01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi:10.21914/anziamj.v57i0.10441
URI: http://eprints.usq.edu.au/id/eprint/36177

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