On the global existence of small data classical solutions to a semilinear wave equation with a time-dependent damping

In this paper, we consider a one-dimension semilinear wave equation with a time-dependent damping and power type nonlinearity, which only depends on the derivatives of the unknown function. Employing the global iteration method, we give a simple proof of the global existence of the small data classical solution to the equation for any given nonlinear power exponent which is bigger than 1.