Abstract :
In this paper we consider the nonlinear viscoelastic equation
utt − u +
t
0
g(t −τ) u(τ )dτ + ut = |u|p−1u in Ω ×(0,∞),
with initial conditions and Dirichlet boundary condition. Under some appropriate assumption
on g, by introducing a potential well we establish the global existence result for
the equation above. Furthermore, we investigate explicit exponential energy decay of the
viscoelastic wave equation under the potential well
