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A singular limit problem for conservation laws related to the Kawahara-Korteweg-de Vries equation

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  • We consider the Kawahara-Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the dispersion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Burgers equation. 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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