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The equation utt − Δu = |u|p for the critical value of p

Published online by Cambridge University Press:  14 November 2011

Jack Schaeffer
Jack Schaeffer
Affiliation:
Department of Mathematics, Carnegie-Mellon University, Pittsburgh, PA 15213, U.S.A.
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Synopsis

The equation utt − Δu = |u|p is considered in two and three space dimensions. Smooth Cauchy data of compact support are given at t = 0. For the case of three space dimensions, John has shown that solutions with sufficiently small data exist globally in time if but that small data solutions blow up in finite time if Glassey has shown the two dimensional case is similar. This paper shows that small data solutions blow up in finite time when p is the critical value, in three dimensions and in two.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 1-2 , 1985 , pp. 31 - 44
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

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