We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
THE LARGE-TIME DEVELOPMENT OF THE SOLUTION TO AN INITIAL-VALUE PROBLEM FOR THE GENERALISED BURGERS' EQUATION.
- Authors
LEACH, J. A.
- Abstract
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.
- Subjects
BURGERS' equation; TIME; DISTANCES; COORDINATES; TANGENTS (Geometry)
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2016, Vol 69, Issue 3, p231
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hbw006