Attractors in confined source problems for coupled nonlinear diffusion

Article

Strunin, Dmitry V.. 2007. "Attractors in confined source problems for coupled nonlinear diffusion." SIAM Journal on Applied Mathematics. 67 (6), pp. 1654-1674. https://doi.org/10.1137/060657923
Article Title

Attractors in confined source problems for coupled nonlinear diffusion

ERA Journal ID393
Article CategoryArticle
Authors
AuthorStrunin, Dmitry V.
Journal TitleSIAM Journal on Applied Mathematics
Journal Citation67 (6), pp. 1654-1674
Number of Pages21
Year2007
Place of PublicationUSA
ISSN0036-1399
1095-712X
Digital Object Identifier (DOI)https://doi.org/10.1137/060657923
Web Address (URL)http://siamdl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=SMJMAP000067000006001654000001&idtype=cvips
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.

Keywordsnonlinear diffusion; attractor; turbulence
ANZSRC Field of Research 2020490302. Numerical analysis
401299. Fluid mechanics and thermal engineering not elsewhere classified
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Byline AffiliationsDepartment of Mathematics and Computing
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