Attractors in confined source problems for coupled nonlinear diffusion

Strunin, Dmitry V. (2007) Attractors in confined source problems for coupled nonlinear diffusion. SIAM Journal on Applied Mathematics, 67 (6). pp. 1654-1674. ISSN 0036-1399

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Abstract

In processes driven by nonlinear diffusion, a signal from a concentrated source is confined in a finite region. Such solutions can be sought in the form of power series in a spatial coordinate. We use this approach in problems involving coupled agents. To test the method, we consider a single equation with (a) linear and (b) quadratic diffusivity in order to recover the known results. The original set of PDEs is converted into a dynamical system with respect to the time-dependent series coefficients. As an application we consider an expansion of a free turbulent jet. Some example trajectories from the respective dynamical system are presented. The structure of the system hints at the existence of an attracting center manifold. The attractor is explicitly found for a reduced version of the system.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright policy of the publisher (SIAM)http://www.siam.org/journals/pdf/copyrite.pdf
Depositing User: Dr Dmitry Strunin
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 29 Apr 2008 07:44
Last Modified: 02 Jul 2013 23:01
Uncontrolled Keywords: nonlinear diffusion; attractor; turbulence
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
09 Engineering > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics
Identification Number or DOI: doi: 10.1137/060657923
URI: http://eprints.usq.edu.au/id/eprint/4115

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