Blow-up of solutions for the dissipative Dullin-Gottwald-Holm equation with arbitrary coefficients

Abstract

We study the Cauchy problem for the weakly dissipative Dullin-Gottwald-Holm equation describing unidirectional propagation of surface waves in a shallow water regime: u(t) - alpha(2)u(xxt) + c(0)u(x) + 3uu(x) + gamma u(xxx) + lambda (u - alpha(2)u(xx)) = alpha(2)(2u(x)u(xx) + uu(xxx)). In the present paper we demonstrate the simple conditions on the initial data that lead to blow-up of the solution in finite time. (C) 2016 Elsevier Inc. All rights reserved.