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

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Wave equation global nonexistence a guess to critical value.
• 年，卷（期）: 2005,（3）
• 页码范围: 263-266
• 页数: 4页
• 分类号: O175.27.
• 语种: 英文

摘要

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.