In this paper we study several qualitative properties of the Degasperis-Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions.
After some remarks on a possible zero-curvature formulation we first establish local well-posedness for the 2-component Camassa-Holm equation. Then precise blow-up scenarios for strong solutions to the system are derived. Finally we present two blow-up results for strong solutions to the system.
This paper is concerned with global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system. A new global existence result and several new blowup results of strong solutions to the system are presented. Our obtained results for the system are sharp and improve considerably earlier results.
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