Mathematics – Analysis of PDEs
Scientific paper
2010-09-07
Mathematics
Analysis of PDEs
31 pages
Scientific paper
We consider the Cauchy-Dirichlet problem for semilinear wave equations in a three space dimensional domain exterior to a bounded and non-trapping obstacle. We obtain a detailed estimate for the lower bound of the lifespan of classical solutions when the size of initial data tends to zero, in a similar spirit to that of the works of John and H\"ormander where the Cauchy problem was treated. We show that our estimate is sharp at least for some special case.
Katayama Soichiro
Kubo Hideo
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