Blow-up of solutions of nonlinear wave equations in three space dimensions
Blow-up of solutions of nonlinear wave equations in three space dimensions
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DOI：
10.1073/pnas.76.4.1559
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发表时间：
1979-04
影响因子：
0.6
通讯作者：
F. John
中科院分区：
文献类型：
--
作者：
F. John
设u(x，t)是解，-u≧A|u|p是x∈IR3，t≧0其中-是d‘Alembertian，A，p是常数A>；0，10，p>；1+√2，如果初始数据具有紧支撑性并且∥u∥在适当的范数下“足够小”，则存在-u=A|u|p的整体解.对于p=2，u变为无穷大的时间为∥u∥−2阶。
Let u(x,t) be a solution, □ u≧A|u|p for x∈IR3, t≧0 where □ is the d'Alembertian, and A, p are constants with A>0, 10, p>1+√2 global solutions of □u=A|u|p exist, if the initial data are of compact support and ∥u∥ is “sufficiently small” in a suitable norm. For p=2 the time at which u becomes infinite is of order ∥u∥−2.