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We consider the Rosenau-Korteweg-de Vries-equation, which contains nonlineardispersive effects. We prove that as the diffusion parameter tends to zero, thesolution of the dispersive equation converge to the discontinous weak solutionsof the Burgers equation. The proof relies on deriving suitable a prioriestimates together with an application of tha compansated compactness method inthe L^p setting.

A singular limit problem for conservation laws related to the Rosenau-Korteweg-de Vries equation