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 G; DI RUVO L. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - (In corso di stampa).

On the convergence of the modified Rosenau and the modified Benjamin-Bona-Mahony equations

COCLITE, Giuseppe Maria;DI RUVO, LORENZO
In corso di stampa

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/144156
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