Average stability and decay properties of forced solutions of the wave propagation problems of classical physics in energy and mean norms
Average stability and decay properties of forced solutions of the wave propagation problems of classical physics in energy and mean norms
复制标题
能量和平均范数经典物理波传播问题强制解的平均稳定性和衰减特性
DOI：
10.1016/0022-247x(89)90034-6
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
William V. Smith
中科院分区：
文献类型：
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作者：
William V. Smith
本文研究了具有含时系数和源项的经典物理波动方程的解在平均意义下稳定的条件。稳定性是在实际上是“能量”和“平均值”这两种意义上寻求的。能量方程是对称双曲方程组的推广，平均值方程是达朗贝尔方程的推广。例如，可以看出，对于最一般类型的系统，解在平均值上具有更大的稳定性。一个事实，这使得我们的方法有点独特的是，没有空间或时间光滑的系数是必需的，我们的结果是很容易扩展到域的形状或有界性没有特殊条件的边界。
This paper seeks conditions under which the solutions of the wave equations of classical physics with time-dependent coefficients and source terms have solutions which are stable in an average sense. Stability is sought in what in practice are the two senses of “energy” and “mean.” The equations for energy are taken as generalizations of the symmetric hyperbolic systems and for the mean sense as generalizations of the d'Alembert equation. It is seen, for example, that solutions have somewhat more stability in the mean for the most general type of system. A fact which makes our approach somewhat unique is that no space or time smoothness of coefficients is required for most of our results and the results are easily extended to domains with boundary with no particular conditions on the shape or boundedness of the domain.