We study the Cauchy problem for the semilinear wave equation in Schwarzschild metric (3+1 dimensional space-time). First, we establish that the problem is locally well--posed and then we prove the blow--up of the solution in two cases: small initial data supported far away from the black hole, large data supported near the black hole. In both cases, we also give an estimate from above for the lifespan of the solution.
Blow Up for the Semilinear Wave Equation in Schwarzschild Metric
GUEORGUIEV, VLADIMIR SIMEONOV
2006
Abstract
We study the Cauchy problem for the semilinear wave equation in Schwarzschild metric (3+1 dimensional space-time). First, we establish that the problem is locally well--posed and then we prove the blow--up of the solution in two cases: small initial data supported far away from the black hole, large data supported near the black hole. In both cases, we also give an estimate from above for the lifespan of the solution.File in questo prodotto:
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