期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1976
卷号：73
期号：2
页码：281-282
DOI：10.1073/pnas.73.2.281
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Strict solutions u of genuinely nonlinear homogeneous hyperbolic equations in two independent variables with initial data f(x) of compact support become singular after a time interval of order ||f||-1. In higher dimensions solutions initially of compact support are likely to have life expectancies of orders ||f||-2+{varepsilon} at least. This is proved for the special case of solutions u(x1..., xn, t) of a second order equation utt={Sigma}i,jaijuxixj, where n [≥] 3 and where the coefficients aij are C{infty}-functions in the first derivatives of u, forming a symmetric positive definite matrix.
关键词：nonlinear wave propagation ; blow up of solutions ; instability
