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.
|Number of pages||19|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Aug 1997|