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2006 Blow-up for the semilinear wave equation in the Schwarzschild metric
Davide Catania, Vladimir Georgiev
Differential Integral Equations 19(7): 799-830 (2006).

Abstract

We study the Cauchy problem for the semilinear wave equation in the Schwarzschild metric ($(3+1)$--dimensional space--time). First, we establish that the problem is locally well posed in $ \mathrm H^\sigma$ for any $\sigma \in [1,p+1)$; then we prove the blow--up of the solution in two cases: a)} $p \in (1,1+\sqrt{2})$ and small initial data supported far away from the black hole, b) $p \in (2,1+\sqrt{2})$ and large data supported near the black hole. In both cases, we also give an estimate from above for the lifespan of the solution.

Citation

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Davide Catania. Vladimir Georgiev. "Blow-up for the semilinear wave equation in the Schwarzschild metric." Differential Integral Equations 19 (7) 799 - 830, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35314
MathSciNet: MR2235896

Subjects:
Primary: 58J45
Secondary: 35B40 , 35L70 , 83C57

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 7 • 2006
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