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Lower bound of the lifespan of solutions to semilinear wave equations in an exterior domain (1009.1188v1)
Published 7 Sep 2010 in math.AP
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 H\"ormander where the Cauchy problem was treated. We show that our estimate is sharp at least for some special case.