Abstract: For the nonlinear wave equation in R^N×R⁺(N≥2): ∂²u(x,t)/∂t²-∂/∂x_i[a_ij(x)∂/∂x_ju=|u|^p-1·u, in 1980 Kato proved the solution of Cauchy problem may blow up in finite time if 1<p≤N+1/N-1. In the present work his result allowing 1<p≤N+3/N-1 is improved by using different estimates.

Key words: condition for blow up, wave equation, Cauchy problem