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Abstract. In this paper, we consider an
initial--boundary value problem for the semilinear dissipative wave
equation in one space dimension of the type :
utt – uxx + |u|m-1ut = V(t)|u|m-1u + f(t, x) in (0, ∞) x (a, b),
where initial data u(0,
x) = u0(x)  H01(a, b), ut(0, x) = u1(x) L2(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).
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Keywords: Global existence, semilinear dissipative
wave equation, nonlinear damping, potential function, source function.
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