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：1979
卷号：76
期号：4
页码：1559-1560
DOI：10.1073/pnas.76.4.1559
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Solutions u(x, t) of the inequality {square}u [≥] A|u|p for x {varepsilon} R3, t [≥] 0 are considered, where {square} is the d'Alembertian, and A,p are constants with A > 0, 1 < p < 1 + {surd}2. It is shown that the support of u is compact and contained in the cone 0 [≤] t [≤] t0 -|x - x0|, if the "initial data" u(x, 0), ut(x, 0) have their support in the ball|x - x0| [≤] t0. In particular, "global" solutions of {square}u = A|u|p with initial data of compact support vanish identically. On the other hand, for A > 0, p > 1 + {surd}2, global solutions of {square}u = A|u|p exist, if the initial data are of compact support and "sufficiently" small.
关键词：asymptotic behavior of solutions ; nonlinear equations and systems ; higher order ; wave equation
