Rigorous derivation and propagation speed property for a two-component Degasperis–Procesi system in shallow water regimes

摘要

We study the propagation speed property for a two-component Degasperis–Procesi system proposed by M. Popowicz. First, we rederive the system from the Euler equation with constant vorticity in shallow water regime. Then, we investigate the propagation behavior of compactly supported solutions, namely whether solutions which are initially compactly supported will retain this property through their lifespan. Finally, we give an exponential decay structure result on the first component function to the system.