NONEXISTENCE OF GLOBAL-SOLUTIONS OF A NONLINEAR HYPERBOLIC SYSTEM

Consider the initial value problem u(tt) = Delta u + \v\(p), v(tt) = D elta v + \u\(q), x is an element of R-n, t > 0, u(x, 0) = f(x), v(x, 0 ) = h(x), u(t)(x, 0) = g(x), v(t)(x, o) = k(x), with 1 less than or eq ual to n less than or equal to 3 and p, q > 0. We show that there exis ts a bound B(n) (less than or equal to infinity) such that if 1 < pq < B(n) all nontrivial solutions with compact support blow up in finite time.