Nonexistence of global solutions for a nonlocal nonlinear hyperbolic system with linear damping

This article concerns the Cauchy problem for the damped nonlinear hyperbolic system where ? > 0 is a small parameter, 0 < α ≤ 1,0 < β ≤ 1,p,q ≥ 1 satisfying pq > 1 , and N ≥ 1 is an integer. It is proved that if N ∕ 2α < max((p + 1) ∕ (pq ? 1),(q + 1) ∕ (pq ? 1)), then every weak solution does not exist globally whenever the initial data satisfy or . Copyright © 2012 John Wiley & Sons, Ltd.