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We study blow-up behavior of solutions for the Cauchy problem of thesemilinear wave equation with time-dependent damping. When the damping iseffective, and the nonlinearity is subcritical, we show the blow-up rates andthe sharp lifespan estimates of solutions. Upper estimates are proved by an ODEargument, and lower estimates are given by a method of scaling variables.

Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity