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 $L^p$ setting.
A singular limit problem for the Rosenau-Korteweg-de Vries-regularized long wave and Rosenau-regularized long wave equations / Coclite, Giuseppe Maria; di Ruvo, L.. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 16:3(2016), pp. 421-437. [10.1515/ans-2015-5034]
A singular limit problem for the Rosenau-Korteweg-de Vries-regularized long wave and Rosenau-regularized long wave equations
COCLITE, Giuseppe Maria;
2016-01-01
Abstract
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 $L^p$ setting.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
