A shallow water wave equation with a weakly dissipative term, which includes the weakly dissipative Camassa-Holm and the weakly dissipative Degasperis-Procesi equations as special cases, is investigated. The sufficient conditions about the existence of the global strong solution are given. Provided that , and , the existence and uniqueness of the global weak solution to the equation are shown to be true.
"The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term." Abstr. Appl. Anal. 2012 (SI11) 1 - 23, 2012. https://doi.org/10.1155/2012/840919