Stability of fronts for a regularization of the Burgers equation

Bhat, H.; Fetecau, R.

doi:10.1090/S0033-569X-08-01099-X

Authors: H. S. Bhat and R. C. Fetecau
Journal: Quart. Appl. Math. 66 (2008), 473-496
MSC (2000): Primary 37K45
DOI: https://doi.org/10.1090/S0033-569X-08-01099-X
Published electronically: July 3, 2008
MathSciNet review: 2445524
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Abstract: We consider the stability of traveling waves for the Leray-type regularization of the Burgers equation that was recently introduced and analyzed by the authors in Bhat and Fetecau (2006). These traveling waves consist of “fronts,” which are monotonic profiles that connect a left state to a right state. The front stability results show that the regularized equation mirrors the physics of rarefaction and shock waves in the Burgers equation. Regarded from this perspective, this work provides additional evidence for the validity of the Leray-type regularization technique applied to the Burgers equation.

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