Energy decay rates of elastic waves in unbounded domain with potential type of damping (Q534721)

An initial value problem for the \(n\)-dimensional system of elastic waves with a power type nonlinearity is considered. For appropriate initial conditions, the system accepts a unique weak solution. Inspired by the method developed in [\textit{R. Ikehata} and \textit{Y. Inoue}, Nonlinear Anal., Theory Methods Appl. 69, No. 4, A, 1396--1401 (2008; Zbl 1149.35010)], and under very special conditions, a total energy decay result is shown. There is also an investigation on asymptotic properties of the linear system of elastic waves in an exterior domain.