On existence and uniqueness of the global weak solution for a shallow water equation

A shallow water equation including the Camassa-Holm and Degasperis-Procesi equations as special cases is investigated. Provided that initial value u0∈H1(R),u0∈L1(R), and (1-∂x2)u0 does not change sign, the existence and uniqueness of global weak solution for the equation are established.