On existence and uniqueness of the global weak solution for a shallow water equation - Guo, Y.; Lai, S.; Wu, Yong Hong (Elsevier Inc., 2012)
A shallow water equation including the Camassa–Holm and Degasperis–Procesi equations as special cases is investigated. Provided that initial value uo ε H1 (R), uo ε L1 (R), and (1 - 2x)uo does not change sign, the existence and uniqueness of global weak solution for the equation are established.