On the behavior of the solution of the dissipative Camassa-Holm equation with the arbitrary dispersion coefficient

In this paper, we consider the dissipative Camassa-Holm equation with arbitrary dispersion coefficient and compactly supported initial data. We demonstrate the simple conditions on the initial data that lead to finite time blow-up of the solution in finite time or guarantee that the solution exists globally. Also, propagation speed for the equation under consideration is investigated. (C) 2014 Elsevier Inc. All rights reserved.