Numerical Comparison of Negative Damping Bounds in a Specified Domain when the Wave Speed Varies

The energy decay of a self-excited wave equation utt - c² ¿ u - P(x)ut = 0 is studied where the wave speed c is greater than one, P(x) ¿ 0, and P(x) L^¿(¿), ¿ ¿ ¿ Rⁿ. Moreover, the relationship between two bounds for negative daming P(x) is a determined domain is shown (n=1,2). Finally some numerical experiences for different P(x) and c are presented for domain ¿ with energy absorbing boundary.