Abstract. In this paper, we consider an
initialboundary value problem for the semilinear dissipative wave
equation in one space dimension of the type :
u_{tt} – u_{xx} + u^{m}^{1}u_{t} = V(t)u^{m}^{1}u + f(t, x) in (0, ∞) x (a, b),
where initial data u(0,
x) = u_{0}(x) H_{0}^{1}(a, b), u_{t}(0, x) = u_{1}(x) L^{2}(a, b) and boundary condition u(t, a) = u(t, b) = 0 for t > 0
with m > 1, on a bounded
interval (a, b). The potential function V(t) is smooth, positive and the
source f(t, x) is bounded. We
investigate the global existence of solution as t > ∞ under certain assumptions on the functions V(t) and f(t, x).

Keywords: Global existence, semilinear dissipative
wave equation, nonlinear damping, potential function, source function.
