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We investigate well-posedness in classes of discontinuous functions for the nonlinear and third order dispersive Degasperis–Procesi equation(DP)∂tu-∂txx3u+4u∂xu=3∂xu∂xx2u+u∂xxx3u.This equation can be regarded as a model for shallow water dynamics and its asymptotic accuracy is the same as for the Camassa–Holm equation (one order more accurate than the KdV equation). We prove existence and L1 stability...
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