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On a strongly damped semilinear wave equation with time-varying source and singular dissipation
Advances in Nonlinear Analysis
This paper deals with the global well-posedness and blow-up phenomena for a strongly damped semilinear wave equation with time-varying source and singular dissipative terms under the null Dirichlet boundary condition. On the basis of cut-off technique, multiplier method, contraction mapping principle, and the modified potential well method, we establish the local well-posedness and obtain the threshold between the existence and nonexistence of the global solution (including the critical case).doi:10.1515/anona-2022-0267 fatcat:pjsbtibc7bf4hgq7za27oi7vdi