Energy decay for the nonlinear wave equation with a half-linear dissipation in $\mathbb{R}^{N}$

Abstract

We study decay estimates of the energy for the nonlinear wave equation in the whole space $\mathbb{R}^{N}$ . The dissipative term consists of the following two parts: The one part is nonlinear in a suitable ball; the other part is linear in the outside of the ball and it may be effective only at infinity. So we may call such a dissipation as a half-linear dissipation. We note that the method of proof is based on the multiplier technique and the unique continuation.