A singular limit problem for the Ibragimov-Shabat equation

Abstract

We consider the Ibragimov-Shabat equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L^p setting

arXiv admin note: text overlap with arXiv:1403.5674, arXiv:1411.0989, arXiv:1411.0616, arXiv:1411.5033