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- W4211100260 abstract "We study the exterior initial–boundary value problem for the linear dissipative wave equation (□+∂t)u=0 in Ω×(0,∞) with (u,∂tu)|t=0=(u0,u1) and u|∂Ω=0, where Ω is an exterior domain in N-dimensional Euclidean space RN. We first show higher local energy decay estimates of the solution u(t), and then, using the cut-off technique together with those estimates, we can obtain the L1 estimate of the solution u(t) when N⩾3, that is, ‖u(t)‖L1(Ω)⩽C(‖u0‖Hn(Ω)+‖u1‖Hn−1(Ω)+‖u0‖Wn,1(Ω)+‖u1‖Wn−1,1(Ω)) for t⩾0, where n=[N/2] is the integer part of N/2. Moreover, by induction argument, we derive the higher energy decay estimates of the solution u(t) for t⩾0." @default.
- W4211100260 created "2022-02-13" @default.
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- W4211100260 date "2007-09-01" @default.
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- W4211100260 doi "https://doi.org/10.1016/j.jmaa.2006.01.031" @default.
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