(untitled) (Journal of Partial Differential Equations, 2005)
Consider the Cauchy problem for a wave equation on R²: u_tt - Δu = |u|^p-1u. In 1981 Glassey gave a guess to a critical value p(2) = 12(3 + 17): when p > p(2) there may exist a global solution and when 1 < p < p(2) the solution may blow up. By our main result in this paper a counter example to the guess is given that the solution may also blow up in finite time even if p(2) < p < 5.