L2-estimates of solutions for damped wave equations with space–time dependent damping term
L2-estimates of solutions for damped wave equations with space–time dependent damping term
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DOI：
10.1016/j.jde.2009.09.022
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发表时间：
2010-01
影响因子：
2.4
通讯作者：
Jiayun Lin;Kenji Nishihara;Jian Zhai
中科院分区：
文献类型：
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作者：
Jiayun Lin;Kenji Nishihara;Jian Zhai
本文考虑具有含时势B（t，x）和吸收半线性项的阻尼波动方程|u| ρ−1u。这里，[公式：见正文]，其中b 0>0，α，β <$0且α+β∈[0，1）。基于局部存在性定理，利用加权能量方法得到了解的整体存在性和L2衰减率。衰变率与Nishihara [K. Nishihara，带吸收半线性项的含空间依赖势的阻尼波方程的衰减性质，预印本]在β=0情形下的结果与Nishihara和翟[K.翟俊，含时阻尼波方程的渐近行为，预印本]，α=0时的数值模拟。
In this paper, we consider the damped wave equation with space–time dependent potential b(t,x) and absorbing semilinear term |u|ρ−1u. Here, [Formula: see text] with b0>0, α,β⩾0 and α+β∈[0,1). Based on the local existence theorem, we obtain the global existence and the L2decay rate of the solution by using the weighted energy method. The decay rate coincides with the result of Nishihara [K. Nishihara, Decay properties for the damped wave equation with space dependent potential and absorbed semilinear term, preprint] in the case of β=0 and coincides with the result of Nishihara and Zhai [K. Nishihara, J. Zhai, Asymptotic behaviors of time dependent damped wave equations, preprint] in the case of α=0.