Semilinear hyperbolic systems violating the null condition

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• 作者：Soichiro Katayama (1)
  Toshiaki Matoba (2)
  Hideaki Sunagawa (3)
  
  1. Department of Mathematics ; Wakayama University ; 930 Sakaedani ; Wakayama ; 640-8510 ; Japan
  2. Osaka Prefectural Tennoji High School ; 2-4-23 Sanmeicho ; Abeno-ku ; Osaka ; 545-0005 ; Japan
  3. Department of Mathematics ; Graduate School of Science ; Osaka University ; 1-1 Machikaneyama-cho ; Toyonaka ; 560-0043 ; Osaka ; Japan
  
• 关键词：35L71 ; 35B40
• 刊名：Mathematische Annalen
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：361
• 期：1-2
• 页码：275-312
• 全文大小：392 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807

文摘

We consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the classical solution under a new structural condition related to the weak null condition. For two-component systems satisfying this condition, we also observe a new kind of asymptotic behavior: Only one component is dissipated and the other one behaves like a non-trivial free solution in the large time.