This note gives a new sufficient condition of the total energy decay for the solutions of the initial-boundary value problems to the dissipative wave equations in exterior domains with non-compactly supported initial data. That condition provides an example of the damping terms of the dissipative wave equations with the total energy decay which has a smaller amplitude than those of all examples derived from a sufficient condition in Mochizuki and Nakazawa [Publ. Res. Inst. Math. Sci. 32 (1996), 401–414].
"A new example of the dissipative wave equations with the total energy decay." Hiroshima Math. J. 46 (2) 187 - 193, July 2016. https://doi.org/10.32917/hmj/1471024948