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In this paper, we consider the wave equation with variable coefficients andboundary damping and supercritical source terms. The goal of this work isdevoted to prove the local and global existence, and classify decay rate ofenergy depending on the growth near zero on the damping term. Moreover, weprove the blow-up of the weak solution with positive initial energy as well asnonpositive initial energy.

Global solutions and blow-up for the wave equation with variable coefficients: II. boundary supercritical source