Consider the Cauchy problem for a wave equation on R^2： 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...Consider the Cauchy problem for a wave equation on R^2： 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.展开更多
文摘Consider the Cauchy problem for a wave equation on R^2： 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.
