2015/01/29 by Coclite, G. M., di Ruvo, L.
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1501.07371
We consider the Rosenau-Korteweg-de Vries-regularized long wave and Rosenau- Korteweg-de Vries equations, which contain nonlinear dispersive effects. We prove that, as the diffusion parameter tends to zero, the solutions of the dispersive equations converge to the unique entropy solution 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 Lp setting.