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

Giuseppe Maria Coclite and Lorenzo di Ruvo

Mathematische Nachrichten, 2018, vol. 291, issue 5-6, 774-792

Abstract: We consider the regularized short†pulse equation, which contains nonlinear dispersive 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.

Date: 2018
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