Revisit to Fritz John’s paper on the blow-up of nonlinear wave equations

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• 作者：Xin Yang ; ^{yangxin1@msu.edu" class="auth_mail" title="E-mail the corresponding author} ; Zhengfang Zhou ^{zfzhou@math.msu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Blow-up ; Wave equations ; Gronwall&rsquo ; s type inequality
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：55
• 期：Complete
• 页码：27-35
• 全文大小：582 K

文摘

In Fritz John’s famous paper (1979), he discovered that for the wave equation □u=∣u∣^p$\square u=\mid u{\mid }^p$, where $1<p<1+\sqrt{2}$ and □$\square$ denoting the d’Alembertian, there is no global solution for any nontrivial and compactly supported initial data. This paper is intended to simplify his proof by applying a Gronwall’s type inequality.