Consider the Cauchy problem for a wave equation on R2:utt-△u =|u|P-1u.In 1981 Glassey gave a guess to a critical value p(2) =1/2(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.
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