The almost global and global existence for quasi-linear wave equations with multiple-propagation speeds in high dimensions |
| |
Authors: | Yi Du Zheng An Yao |
| |
Institution: | [1]School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China [2]School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, P. R. China |
| |
Abstract: | 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. |
| |
Keywords: | Nonlinear wave equations multiple-speeds small amplitude high dimensions |
本文献已被 维普 SpringerLink 等数据库收录! |
|