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

We consider the regularized short-pulse equation, which contains nonlinear dis- persive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the short-pulse one. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting.