Hyperbolic Systems with Discontinuous Coefficients: Generalized Wavefront Sets
Hyperbolic Systems with Discontinuous Coefficients: Generalized Wavefront Sets
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具有不连续系数的双曲系统：广义波前集
DOI：
10.1007/978-3-7643-8969-7_7
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
M. Oberguggenberger
中科院分区：
文献类型：
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作者：
M. Oberguggenberger
我们研究具有非光滑、可能不连续符号和分布数据的伪微分方程的线性双曲系统。本文提出了一种方法，通过广义函数的哥伦博代数的对偶来构造解。我们计算以不连续传播速度和 delta 函数作为初始数据的输运方程解的广义波前集。广义波前集被证明比相应分布极限的波前集具有更精细和信息丰富的结构。
We study linear hyperbolic systems of pseudo-differential equations with nonsmooth, possibly discontinuous symbols and distributional data. This note initiates an approach whereby solutions are constructed in the dual of the Colombeau algebra of generalized functions. We compute the generalized wave front set of the solution to a transport equation with discontinuous propagation speed and delta functions as initial data. The generalized wave front set turns out to have a more refined and informative structure than the wavefront set of the corresponding distributional limit.