Abstract
This paper is concerned with several aspects of the existence of global solutions and the formation of singularities for the Degasperis-Procesi equation on the line. Global strong solutions to the equation are determined for a class of initial profiles. On the other hand, it is shown that the first blow-up can occur only in the form of wave-breaking. A new wave-breaking mechanism for solutions is described in detail and two results of blow-up solutions with certain initial profiles are established.
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Liu, Y., Yin, Z. Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation. Commun. Math. Phys. 267, 801–820 (2006). https://doi.org/10.1007/s00220-006-0082-5
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DOI: https://doi.org/10.1007/s00220-006-0082-5