Nonlinear stability in seismic waves

Article

Ali, Adham A. and Strunin, Dmitry V.. 2017. "Nonlinear stability in seismic waves." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 57, pp. C382-C397. https://doi.org/10.21914/anziamj.v57i0.10441
Article Title

Nonlinear stability in seismic waves

ERA Journal ID43
Article CategoryArticle
AuthorsAli, Adham A. (Author) and Strunin, Dmitry V. (Author)
Journal TitleAustralian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal
Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal
Journal Citation57, pp. C382-C397
Number of Pages16
Year2017
Place of PublicationAustralia
ISSN1446-1811
1446-8735
Digital Object Identifier (DOI)https://doi.org/10.21914/anziamj.v57i0.10441
Web Address (URL)https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10441
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.

ANZSRC Field of Research 2020490105. Dynamical systems in applications
Public Notes

Article published in 2017, in the vol. 57 2015 issue of The ANZIAM Journal. Published version deposited in accordance with the copyright policy of the publisher. Published as part of the Proceedings of the 12th Biennial Engineering Mathematics and Applications Conference.

Byline AffiliationsSchool of Agricultural, Computational and Environmental Sciences
Institution of OriginUniversity of Southern Queensland
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