Abstract
We consider the Burgers equation with a nonhomogeneous drift term, in the limit of small dissipation. A finite-dimensional manifold of slowly varying shock-like solutions is described, and a formal derivation of the dynamics on this manifold, in terms of a system of ordinary differential equations, is given. We also discuss the interpretation of the stationary solutions to the Burgers equation imbedded on the slow manifold.
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Wolansky, G. On the slow evolution of quasi-stationary shock waves. J Dyn Diff Equat 6, 247–276 (1994). https://doi.org/10.1007/BF02218530
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DOI: https://doi.org/10.1007/BF02218530