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We consider the Rosenau equation, which contains nonlinear dispersiveeffects. We prove that as the diffusion parameter tends to zero, the solutionsof the dispersive equation converge to discontinuous weak solution of theBurgers equation. The proof relies on deriving suitable a priori estimatestogether with an application of the compensated compactness method in the L^psetting.

A singular limit problem for conservation laws related to the Rosenau equation