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Effects of a saturating dissipation in Burgers-type equations

✍ Scribed by A. Kurganov; P. Rosenau

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 193 KB
Volume: 50
Category: Article
ISSN: 0010-3640
DOI: 10.1002/(sici)1097-0312(199708)50:8<753::aid-cpa2>3.0.co;2-5

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✦ Synopsis

We propose and study a new variant of the Burgers equation with dissipation fluxes that saturate as the gradients become unbounded. If the upstream-downstream transition is above a critical threshold, the corresponding Riemann problem admits a weak solution wherein part of the transit is accomplished by a jump. It is shown that the solution to a Cauchy problem with sufficiently small compact or periodic initial data preserves its initial smoothness.

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