We consider the modified Rosenau and the modified Benjamin-Bona-Mahony equations, which contain nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equations converge to entropy solutions of a scalar conservation laws. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $L^p$ setting.
On the convergence of the modified Rosenau and the modified Benjamin-Bona-Mahony equations / Coclite, Giuseppe Maria; di Ruvo, Lorenzo. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - 74:5(2017), pp. 899-919. [10.1016/j.camwa.2016.02.016]
On the convergence of the modified Rosenau and the modified Benjamin-Bona-Mahony equations
Coclite, Giuseppe Maria;
2017-01-01
Abstract
We consider the modified Rosenau and the modified Benjamin-Bona-Mahony equations, which contain nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equations converge to entropy solutions of a scalar conservation laws. 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.
