Lower bound of the lifespan of solutions to semilinear wave equations in an exterior domain

Details Lower bound of the lifespan of solutions to semilinear wave equations in an exterior domain Lower bound of the lifespan of solutions to semilinear wave equations in an exterior domain

2010-09-07

arxiv.org/abs/1009.1188v1

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.

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