Low-dimensional modelling of a generalised Burgers equation

Li, Zhenquan and Roberts, A. J. (2007) Low-dimensional modelling of a generalised Burgers equation. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 203-218. ISSN 0973-1768

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Abstract

Burgers equation is one of the simplest nonlinear partial differential equations—it combines the basic processes of diffusion and nonlinear steepening. In some applications it is appropriate for the diffusion coefficient to be a time-dependent function. Using a Wayne's transformation and centre manifold theory, we derive 1-mode and 2-mode centre manifold models of the generalized Burgers equations for bounded smooth time dependent coefficients. These modelings give some interesting extensions to existing results such as the similarity solutions using the similarity method.

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Item Type:	Article (Commonwealth Reporting Category C)
Refereed:	Yes
Item Status:	Live Archive
Additional Information:	Submitted Version made accessible, and also available at http://arxiv.org/ftp/math-ph/papers/0307/0307064.pdf
Faculty/School / Institute/Centre:	Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Faculty/School / Institute/Centre:	Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Date Deposited:	20 Apr 2010 12:49
Last Modified:	14 Jun 2016 01:00
Uncontrolled Keywords:	differential equations; nonlinear models (statistics); binomial coefficients; diffusion
Fields of Research (2008):	01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling 02 Physical Sciences > 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics > 020299 Atomic, Molecular, Nuclear, Particle and Plasma Physics not elsewhere classified 01 Mathematical Sciences > 0101 Pure Mathematics > 010107 Mathematical Logic, Set Theory, Lattices and Universal Algebra 01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
Fields of Research (2020):	49 MATHEMATICAL SCIENCES > 4905 Statistics > 490510 Stochastic analysis and modelling 51 PHYSICAL SCIENCES > 5107 Particle and high energy physics > 510799 Particle and high energy physics not elsewhere classified 49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490407 Mathematical logic, set theory, lattices and universal algebra 49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490410 Partial differential equations
Socio-Economic Objectives (2008):	E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI:	http://eprints.usq.edu.au/id/eprint/7528

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