Global weak solutions and wave breaking phenomena to the periodic Degasperis–Procesi equation with strong dispersion

Considered herein is the initial-value problem for the periodic Degasperis–Procesi equation with a strong dispersive term that is an approximation to the incompressible Euler equation for shallow water waves. The existence and uniqueness of global weak solutions are established. Moreover, the periodic peakon and shockpeakon solutions of the equation are constructed.