The Large-Time Solution of Burgers' Equation with Time- Dependent Coefficients. II. Algebraic Coefficients

F. B Ali Sulaiman; J. A. Leach; D. J. Needham

doi:10.1111/sapm.12130

The Large-Time Solution of Burgers' Equation with Time- Dependent Coefficients. II. Algebraic Coefficients

F. B Ali Sulaiman, J. A. Leach^*, D. J. Needham

^*Corresponding author for this work

Mathematics

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Abstract

In this paper, we consider an initial-value problem for Burgers' equation with variable coefficients ut+Φ(t)uux=Ψ(t)uxx,-∞0,where x and t represent dimensionless distance and time, respectively, while Ψ(t), Φ(t) are given continuous functions of t ( > 0). In particular, we consider the case when the initial data has algebraic decay as |x|→∞, with u(x,t)→u+ as x→∞ and u(x,t)→u- as x→-∞. The constant states u+ and u-(≠u+) are problem parameters. We focus attention on the case when Φ(t)=tδ (with δ>-1) and Ψ(t)=1. The method of matched asymptotic coordinate expansions is used to obtain the large-t asymptotic structure of the solution to the initial-value problem over all parameter values.

Original language	English
Pages (from-to)	163-188
Journal	Studies in Applied Mathematics
Volume	136
Issue number	2
Early online date	2 Jun 2016
DOIs	https://doi.org/10.1111/sapm.12130
Publication status	E-pub ahead of print - 2 Jun 2016

ASJC Scopus subject areas

Applied Mathematics

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10.1111/sapm.12130Licence: None: All rights reserved

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Checked for eligibility: 31/05/2016. This is the peer reviewed version of the following article: Leach, J. A. (2016), The Large-Time Solution of Burgers' Equation with Time-Dependent Coefficients. I. The Coefficients Are Exponential Functions. Studies in Applied Mathematics, 136: 163–188., which has been published in final form at doi: 10.1111/sapm.12098. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Accepted author manuscript, 376 KBLicence: None: All rights reserved

Cite this

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The Large-Time Solution of Burgers' Equation with Time- Dependent Coefficients. II. Algebraic Coefficients

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