A quarter-plane problem for the modified Burgers' equation.
In: Journal of Mathematical Physics, Jg. 54 (2013-09-01), Heft 9, S. 91502-91518
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Zugriff:
In this paper, we address an initial-boundary value problem for the modified Burgers' equation. The normalized modified Burgers' equation considered is given by ut + up ux - uxx = 0, 0 < x < ∞, t > 0, where x and t represent dimensionless distance and time, respectively, and p (>1) is a parameter. In particular, we consider the case when the initial and boundary conditions are given by u(x, 0) = ui for 0 < x < ∞ and u(0, t) = ub for t > 0, respectively. We initially focus attention on the case when ui = 0 and ub > 0. In this case, the method of matched asymptotic coordinate expansions is used to obtain the complete large-t asymptotic structure of the solution to this problem, which exhibits the formation of a permanent form travelling wave solution propagating with speed v=u b p /p+1 (>0) and connecting u = 0 ahead of the wave-front to u = ub at the rear of the wave. Further, the asymptotic correction to the propagation speed is of O t -3/2 exp -v 2 /4t as t → ∞, and the rate of convergence of the solution of the initial-boundary value problem to the travelling wave is O t -3/2 exp -v 2 /4t as t → ∞. We conclude the paper with a discussion of the structure of the large-time solution to the initial-boundary value problem for general values of ub and ui (excluding the trivial case when ui = ub). [ABSTRACT FROM AUTHOR]
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Titel: |
A quarter-plane problem for the modified Burgers' equation.
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Autor/in / Beteiligte Person: | Leach, J. A. |
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Zeitschrift: | Journal of Mathematical Physics, Jg. 54 (2013-09-01), Heft 9, S. 91502-91518 |
Veröffentlichung: | 2013 |
Medientyp: | academicJournal |
ISSN: | 0022-2488 (print) |
DOI: | 10.1063/1.4820787 |
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