Date of this Version
Indiana University Mathematics Journal copyright , Vol. 51, No. 6 (2002)
In this article we focus on the global well-posedness of an initial-boundary value problem for a nonlinear wave equation in all space dimensions. The nonlinearity in the equation features the damping term |u|k |ut|m sgn(ut) and a source term of the form |u|p-1u, where k, p ≥ 1 and 0 < m < 1. In addition, if the space dimension n ≥ 3, then the parameters k, m and p satisfy p, k/(1-m) ≤ n/(n - 2). We show that whenever k + m ≥ p, then local weak solutions are global. On the other hand, we prove that whenever p > k + m and the initial energy is negative, then local weak solutions blow-up in finite time, regardless of the size of the initial data.