On Second Order Hyperbolic Equations with Coefficients Degenerating at Infinity and the Loss of Derivatives and Decays
On Second Order Hyperbolic Equations with Coefficients Degenerating at Infinity and the Loss of Derivatives and Decays
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关于系数无穷大简并及导数损失和衰变的二阶双曲方程
DOI：
10.1016/j.jde.2016.08.019
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
T. Kinoshita
中科院分区：
文献类型：
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作者：
T. Kinoshita
本文研究了∂t2u−a(t，x)∂x2u=0波动方程在[0，T]×Rx上柯西问题在加权L 2空间中的适定性问题。对于所有(t，x)∈[0，T]×Rx，我们给出了条件a(t，x)>；0，它介于严格双曲条件和弱双曲条件之间，并允许衰减系数a(t，x)使得对所有t→∞[0，T]都有Lim|x|∈a(t，x)=0。我们担心的是衍生品的损失和解决方案的衰落。
In this paper, we study well-posedness issues in the weighted L 2 space for the Cauchy problem on [0, T]× R x for wave equations of the form∂ t 2 u− a (t, x)∂ x 2 u= 0. We shall give the condition a (t, x)> 0 for all (t, x)∈[0, T]× R x which is between the strictly hyperbolic condition and weakly hyperbolic one, and allows the decaying coefficient a (t, x) such that lim| x|→∞ a (t, x)= 0 for all t∈[0, T]. Our concerns are the loss of derivatives and decays of the solutions.