Uniform Energy Decay for Wave Equations with Unbounded Damping Coefficients
Uniform Energy Decay for Wave Equations with Unbounded Damping Coefficients
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DOI：
10.1619/fesi.63.133
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发表时间：
2017-06
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影响因子：
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通讯作者：
R. Ikehata;H. Takeda
中科院分区：
文献类型：
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作者：
R. Ikehata;H. Takeda
本文考虑了全空间中具有无界阻尼系数的波动方程的Cauchy问题。对于一般的无界阻尼系数，我们得到了一致的总能量衰减估计以及弱解的唯一存在性结果。在这种情况下，我们从来没有强加强有力的假设，如紧的支持的初始数据。这意味着，我们从来没有依赖于有限的传播速度属性的解决方案，我们试图处理一个基本的无界系数的情况。
We consider the Cauchy problem for wave equations with unbounded damping coefficients in the whole space. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence result of a weak solution. In this case we never impose strong assumptions such as compactness of the support of the initial data. This means that we never rely on the finite propagation speed property of the solution, and we try to deal with an essential unbounded coefficient case.