General energy decay for wave equation with space-time potential and time delay in Rn

In this paper, we consider the following wave equation u tt - Δ u + a 0 b ( t , x ) u t + a 1 b ( t , x ) u t ( t - τ ) + | u | p - 1 u = 0 , t > 0 , x ∈ R n u ( 0 , x ) = u 0 ( x ) , u t ( 0 , x ) = u 1 ( x ) x ∈ R n u t ( t - τ , x ) = h 0 ( t - τ , x ) , x ∈ R n , 0 < t < τ , with space time dependent potential and a time delay in the internal feedback. Under appropriate conditions on the damping coefficients b and the constants a 0 , a 1 , we establish a general energy decay result of the solution where the initial data have compact support.