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We consider a damped wave equation in a bounded domain. The damping isnonlinear and is homogeneous with degree p -- 1 with p > 2. First, we show thatthe energy of the strong solution in the supercritical case decays as anegative power of t; the rate of decay is the same as in the subcritical orcritical cases, provided that the space dimension does not exceed ten. Next,relying on a new differential inequality, we show that if the initialdisplacement is further required to lie in L p , then the energy of thecorresponding weak solution decays logarithmically in the supercritical case.Those new results complement those in the literature and open an importantbreach in the unknown land of super-critical damping mechanisms.

Energy decay estimates for the wave equation with supercritical nonlinear damping