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arXiv · 1009.1188

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

Soichiro Katayama·Hideo Kubo
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Abstract

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 Hörmander where the Cauchy problem was treated. We show that our estimate is sharp at least for some special case.

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Soichiro Katayama, Hideo Kubo. 2010-09-07. Lower bound of the lifespan of solutions to semilinear wave equations in an exterior domain. https://arxiv.org/abs/1009.1188

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