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We consider the regularized short-pulse equation, which contains nonlineardis- persive effects. We prove that as the diffusion parameter tends to zero,the solutions of the dispersive equation converge to discontinuous weaksolutions of the short-pulse one. The proof relies on deriving suitable apriori estimates together with an application of the compensated compactnessmethod in the Lp setting.

Convergence of the regularized short pulse equation to the short pulse one