Semilinear hyperbolic systems violating the null condition |
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Authors: | Soichiro Katayama Toshiaki Matoba Hideaki Sunagawa |
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Institution: | 1.Department of Mathematics,Wakayama University,Wakayama,Japan;2.Osaka Prefectural Tennoji High School,Osaka,Japan;3.Department of Mathematics, Graduate School of Science,Osaka University,Toyonaka,Japan |
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Abstract: | 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. |
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