The global existence for semilinear wave equations with space-dependent critical damping at u - Au + iv4 atu = f(u) in an exterior domain is dealt with, where f(u)= IuIP-lu and f(u) = IuV' are in mind. Ex-istence and non-existence of global-in-time solutions are discussed. To obtain global existence, a weighted energy estimate for the linear problem is crucial. The proof of such a weighted energy estimate contains an alternative proof of energy estimates established by Ikehata-Todorova-Yordanov J. Math. Soc. Japan (2013), 183-236 but the argument in this paper clarifies the precise dependence of the location of the support of initial data. The blowup phe-nomena are verified by using a test function method with positive harmonic functions satisfying the Dirichlet boundary condition.
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机译：本文讨论了在外域中 u - Au + iv4 atu = f（u） 处具有空间相关临界阻尼的半线性波动方程的全局存在性，其中 f（u）= IuIP-lu 和 f（u） = IuV'。讨论了全局时间解决方案的现有和不存在。为了获得全局存在，线性问题的加权能量估计至关重要。这种加权能量估计的证明包含Ikehata-Todorova-Yordanov [J. Math. Soc. Japan （2013）， 183-236]建立的能量估计的替代证明，但本文的论点澄清了初始数据支持位置的精确依赖性。采用满足狄利克雷边界条件的正谐波函数测试函数方法验证了爆炸值。
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