ON INITIAL BOUNDARY VALUE PROBLEMS FOR THE DEGENERATE 1D WAVE EQUATION
ON INITIAL BOUNDARY VALUE PROBLEMS FOR THE DEGENERATE 1D WAVE EQUATION
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简并一维波动方程的初始边值问题
DOI：
10.15421/141906
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发表时间：
2019
影响因子：
--
通讯作者：
V. V. Borsch
中科院分区：
文献类型：
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作者：
V. V. Borsch
在时空矩形中，二阶光滑系数函数a（x）的线性非齐次退化波动方程的初边值问题在单点段上为零.利用方程的正则化方法和特征线理论证明了初边值问题的适定性。波动方程的问题则归结为一阶偏微分方程的双曲平衡律2和3的问题。利用适当的数值方法得到了问题的弱解。一些方法正则化所获得的结果。
Initial boundary value problems in space-time rectangle for the following linear inhomogeneous degenerate wave equation of the second order smooth coefficient function a(x) vanishes in single points of segment. The well-posedness of the initial boundary value problems is achieved using some approaches to regularization of the equation and the theory of characteristics. The problems for wave equation are then reduced to problems for hyperbolic balance laws 2 and 3 of partial differential equations of the first order. Weak solutions to the problems are obtained using proper numerical methods. Results obtained for some approaches to regularization are presented.