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We consider blow-up results for a system of inhomogeneous wave inequalitiesin exterior domains. We will handle three type boundary conditions: Dirichlettype, Neumann type and mixed boundary conditions. We use a unified approach toshow the optimal criteria of Fujita type for each case. Our study yieldsnaturally optimal nonexistence results for the corresponding stationary wavesystem and equation. We provide many new results and close some open questions.

Critical criteria of Fujita type for a system of inhomogeneous wave inequalities in exterior domains