Blow-up for nonlinear dissipative wave equations in R^n

We consider the Cauchy problem u_tt-Delta u +|u_t|^{m-1}u_t=|u|^{p-1}u, in (0,infty) x R^n, u(0,x)=u_0(x), u_t(0,x)=v_0(x) for 1<= m<p, p<n/(n-2) for n\ge 3. We prove that for any given numbers alpha0, lambda>=0 there exist infinitely many data u_0, v_0 in the energy space such that the initial energy E(0)=\lambda, the gradient norm |\nabla u_0\|_2=\alpha, and the solution of the above Cauchy problem blows up in finite time.