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Blow-up for quasi-linear wave equations in three space dimensions

✍ Scribed by Fritz John

Publisher
John Wiley and Sons
Year
1981
Tongue
English
Weight
621 KB
Volume
34
Category
Article
ISSN
0010-3640

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✦ Synopsis

0010-13640/81/00344029S2.30 'I$ need not even be defined for all arguments, since u' and u" will stay small for sufficiently small norms off, g. 2Solutions of the one-dimensional problem (4a, b) can also be viewed as special solutions u(x.r) of the n-dimensional equation u,, = c(u,,)Au which happen not to depend on x 2 , . . . , x,,. Their blow-up does not contradict Klainerrnan's theorem, since their initial data as functions in R" do not have finite L1-norms. 'The assumption on u,,(x, 0) is needed in some cases. For example for C = u i we have the global non-trivial solution u = f t 2 with vanishing initial data.

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