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

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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
172 Downloads (Pure)

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 languageEnglish
Pages (from-to)163-188
JournalStudies in Applied Mathematics
Volume136
Issue number2
Early online date2 Jun 2016
DOIs
Publication statusE-pub ahead of print - 2 Jun 2016

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint

Dive into the research topics of 'The Large-Time Solution of Burgers' Equation with Time- Dependent Coefficients. II. Algebraic Coefficients'. Together they form a unique fingerprint.

Cite this