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In this paper, we consider a wave equation with logarithmic source term and fractional boundary dissipation. We study the global existence of the solution under some conditions and prove the general decay of the solution in this case by using the Lyapunov functional. Also, the blow-up of solution is established at three different levels of energy using the potential well method.

Global existence, general decay and blow-up for a nonlinear wave equation with logarithmic source term and fractional boundary dissipation