We consider the Rosenau-Korteweg-de Vries 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 the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the $L^p$ compensated compactness method.
A singular limit problem for conservation laws related to the Rosenau-Korteweg-de Vries equation / Coclite, Giuseppe Maria; di Ruvo, L.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 107:3(2017), pp. 315-335. [10.1016/j.matpur.2016.07.002]
A singular limit problem for conservation laws related to the Rosenau-Korteweg-de Vries equation
COCLITE, Giuseppe Maria;
2017-01-01
Abstract
We consider the Rosenau-Korteweg-de Vries 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 the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the $L^p$ compensated compactness method.| File | Dimensione | Formato | |
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