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In this paper, we consider the Cauchy problem for systems of quasi-linear wave equations with multiple propagation speeds
in spatial dimensions n ≥ 4. The problem when the nonlinearities depend on both the unknown function and their derivatives is studied. Based on some
Klainerman-Sideris type weighted estimates and space-time L
2 estimates, the results that the almost global existence for space dimensions n = 4 and global existence for n ≥ 5 of small amplitude solutions are presented. 相似文献
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