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The Almost Global and Global Existence for Quasi-linear Wave Equations with Multiple-Propagation Speeds in High Dimensions

The Almost Global and Global Existence for Quasi-linear Wave Equations with Multiple-Propagation Speeds in High Dimensions
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摘要 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 L2 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. 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 L2 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.
作者 Yi DU Zheng An YAO
机构地区 School of Mathematical Sciences School of Mathematics and Computational Science
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第6期1205-1220,共16页 数学学报（英文版）
基金 The first author is supported by National Natural Science Foundation of China （Grant No. 10826069） and China Postdoctoral Foundation （Grant No. 20090450902） the second author is supported by National Natural Science Foundation of China （Grant Nos. 10471156 and 10531040）
关键词 Nonlinear wave equations multiple-speeds small amplitude high dimensions Nonlinear wave equations, multiple-speeds, small amplitude, high dimensions
分类号 O175.29 [理学—基础数学] TP393.08 [自动化与计算机技术—计算机应用技术]
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Acta Mathematica Sinica,English Series
2011年 第6期

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