A singular limit problem for the Ibragimov-Shabat equation

2014/11/19 by Coclite, G. M., di Ruvo, L.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1411.5167

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

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