Convergence result for the short pulse equation

In this paper, we consider a non-local elliptic-hyperbolic system related to the short pulse equation. It is a model which describes the evolution of the electrical field of linearly polarized continuum spectrum pulses in optical waveguides, including fused-silica telecommunication- type or photonic-crystal fibers, as well as hollow capillaries filled with transparent gases. We prove that the solution of a non-local elliptic-hyperbolic system related to the short pulse equation converges to the unique entropy one of the short pulse equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L p setting.