A singular limit problem for the Kudryashov-Sinelshchikov equation

Abstract

We consider the Kudryashov-Sinelshchikov equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation coverge to the entropy ones of the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the compansated compactness method in the L^p setting.