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A singular limit problem for the Ibragimov-Shabat equation

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  • 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.
    Mathematics Subject Classification: Primary: 35G25, 35L65; Secondary: 35L05.

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