THE LARGE-TIME DEVELOPMENT OF THE SOLUTION TO AN INITIAL-VALUE PROBLEM FOR THE GENERALISED BURGERS' EQUATION.
In: Quarterly Journal of Mechanics & Applied Mathematics, Jg. 69 (2016-08-01), Heft 3, S. 231-256
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Zugriff:
In this article, we consider an initial-value problem for the generalized Burgers' equation. The normalized Burgers' equation considered is given by ut + tδuux = uxx, -∞ < x < ∞, t > 0, where −1/2 ≤ δ ≠ 0, and x and t represent dimensionless distance and time respectively. In particular, we consider the case when the initial data has a discontinuous step, where u(x, 0) = u+ for x ≥ 0 and u(x, 0) = u− for x < 0, where u+ and u− are problem parameters with u+ ≠ u−. The method of matched asymptotic coordinate expansions is used to obtain the large-t asymptotic structure of the solution to this problem, which exhibits a range of large-t attractors depending on the problem parameters. Specifically, the solution of the initial-value problem exhibits the formation of (i) an expansion wave when δ > −1/2 and u+ > u-, (ii) a Taylor shock (hyperbolic tangent) profile when δ > −1/2 and u+ < u− and (iii) the Rudenko-Soluyan similarity solution when δ = −1/2. [ABSTRACT FROM AUTHOR]
Titel: |
THE LARGE-TIME DEVELOPMENT OF THE SOLUTION TO AN INITIAL-VALUE PROBLEM FOR THE GENERALISED BURGERS' EQUATION.
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Autor/in / Beteiligte Person: | LEACH, J. A. |
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Zeitschrift: | Quarterly Journal of Mechanics & Applied Mathematics, Jg. 69 (2016-08-01), Heft 3, S. 231-256 |
Veröffentlichung: | 2016 |
Medientyp: | academicJournal |
ISSN: | 0033-5614 (print) |
DOI: | 10.1093/qjmam/hbw006 |
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