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arXiv · 1411.5167

A singular limit problem for the Ibragimov-Shabat equation

G. M. Coclite·L. di Ruvo
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Abstract

We consider the Ibragimov-Shabat 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 a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L^p setting

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G. M. Coclite, L. di Ruvo. 2014-11-19. A singular limit problem for the Ibragimov-Shabat equation. https://arxiv.org/abs/1411.5167

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