A CRITICAL VALUE FOR GLOBAL NONEXISTENCE OF SOLUTION OF A WAVE EQUATION

摘要

Consider the Cauchy problem for a wave equation on R~2: u_(tt) — Δu = |u|~(p-1)u. In 1981 Glassey gave a guess to a critical value p(2) = 1/2 (3 + (17)~(1/2)): 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.