Effects of a saturating dissipation in Burgers-type equations

A. Kurganov, P. Rosenau

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)753-771
Number of pages19
JournalCommunications on Pure and Applied Mathematics
Volume50
Issue number8
DOIs
StatePublished - Aug 1997

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