The existence of global weak solutions to the Cauchy problem for a generalized Camassa-Holm equation with a dissipative term is investigated in the space × ; provided that its initial value belongs to the space . A one-sided super bound estimate and a space-time higher-norm estimate on the first-order derivatives of the solution with respect to the space variable are derived.
"The Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation." Abstr. Appl. Anal. 2012 (SI06) 1 - 21, 2012. https://doi.org/10.1155/2012/693010