Global existence, asymptotic behaviour, and global non-existence of solutions for damped non-linear wave equations of Kirchhoff type in the whole space

We study the global existence, asymptotic behaviour, and global non-existence (blow-up) of solutions for the damped non-linear wave equation of Kirchhoff type in the whole space: u(u) + u, = (a + b\\del u\\(2 gamma))Delta u + \u\(x)u in R-N x R+, for a, b greater than or equal to 0, a + b > 0, gamma greater than or equal to 1, and alpha > 0, with initial data u(x, 0) = u(0)(x) and u,(x, 0) = u,(x). Copyright (C) 2000 John Wiley & Sons, Ltd.