MR2154379
Kubo, Hideo and Ohta, Masahito
Hideo KUBO and Masahito OHTA
On Systems of Semilinear Wave Equations with Unequal Propagation Speeds in Three Space Dimensions
Funkcialaj Ekvacioj. Serio Internacia
48
2005
65--98
http://fe.math.kobe-u.ac.jp/FE/FullPapers/48-1/48_65.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2154379
In this paper we study coupled systems of semilinear wave equations and derive sharp conditions for the small data global existence and blowup for the system. The way of the interaction in the nonlinearities plays an important role to determine the condition. We focus on the case where propagation speeds also come into play. The discrepancy of the speeds is actually essential in Theorem 3.1 for instance. Moreover, in some cases we have different conclusion for the same nonlinearity according to the order of them. To handle such cases, we modify the argument presented by F. John [12].
System of semilinear wave equations, Global existence, Blowup, Lifespan.
35L70, 35B40.
48-65
2005
On Systems of Semilinear Wave Equations with Unequal Propagation Speeds in Three Space Dimensions
KUBO, Hideo and OHTA, Masahito
Hideo KUBO and Masahito OHTA
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