Decay character and global existence for weakly coupled system of semilinear σ$\sigma$‐evolution damped equations with time‐dependent damping

Abstract In this article, we investigate the existence and decay rate of the global solution to the coupled system of semilinear structurally damped ‐evolution equations with time‐dependent damping in the so‐called effective cases We obtain conditions for the existence and the decay estimates of the global (in time) solution that are expressed in terms of the decay character of the initial data and . Furthermore, the blow‐up results for solutions to the semilinear problem also presented.