Energy decay for the linear and semilinear wave equations in exterior domains with some localized dissipations
Energy decay for the linear and semilinear wave equations in exterior domains with some localized dissipations
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DOI：
10.1007/s002090100275
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发表时间：
2001-12
影响因子：
0.8
通讯作者：
M. Nakao
中科院分区：
文献类型：
--
作者：
M. Nakao
本文导出了波动方程初边值问题解的总能量衰减和有界性，其中u（x，0）=u_0（x），u_t（x，0）=u_1（x）\mbox{ and } u|_{\partial \Omega}=0$，其中anda（x）是一个非负函数，它在边界的某些部分和无穷远处是正的。我们应用这些估计证明了具有非线性项f（u）like的半线性波动方程的整体衰减解的存在性。我们注意到边界上没有任何几何条件。
We derive the total energy decayandboundednessfor the solutions to the initial boundary value problem for the wave equation in an exterior domain:with $u(x,0)=u_0(x), u_t(x,0)=u_1(x) \mbox{ and } u|_{\partial \Omega}=0$, whereanda(x) is a nonnegative function which is positive near some part of the boundaryand near infinity. We apply these estimates to prove the global existence of decaying solutions for semilinear wave equations with nonlinearityf(u) like. We note that no geometrical condition is imposed on the boundary.