Total energy decay for semilinear wave equations with a critical potential type of damping Original Research Article

We consider the Cauchy problem for semilinear wave equations with a critical potential type of damping coefficient (1+|x|)−1(1+|x|)−1 in View the MathML sourceRN and a power nonlinearity |u|p−1u|u|p−1u. We shall derive total energy and LpLp decay estimates in the case when the initial data have a compact support.