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

Article type: Research Article

Authors: Jung, Il Hyo | Kang, Yong Han

Affiliations: Department of Mathematics, Pusan National University, Pusan 609-735, South Korea E-mail: ilhjung@pusan.ac.kr | Department of Mathematics, University of Ulsan, Ulsan 680-749, South Korea E-mail: yonghann@mail.ulsan.ac.kr

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.

Keywords: nonlinear wave equation, energy decay, Cauchy problem

Journal: Asymptotic Analysis, vol. 48, no. 1-2, pp. 19-32, 2006