Diffraction of singularities for the wave equation on manifolds with corners
Diffraction of singularities for the wave equation on manifolds with corners
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带角流形上波动方程的奇点衍射
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
J. Wunsch
中科院分区：
文献类型：
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作者：
R. Melrose;A. Vasy;J. Wunsch
我们考虑具有任意余维角点的流形上波动方程的基本解。如果解的初始极点位于适当的位置，我们证明了被角衍射的奇点（即，不严格地说，不沿着横向反射光线的极限传播）比解的主要奇点更平滑。更一般地说，我们表明，受非聚焦的假设，衍射波前的波动方程的任何解决方案是光滑的比入射奇点。这些结果扩展了我们以前的工作的边缘流形的情况下，纤维的边界纤维化，在这里得到的问题的角落爆破，本身是流形的角落。
We consider the fundamental solution to the wave equation on a manifold with corners of arbitrary codimension. If the initial pole of the solution is appropriately situated, we show that the singularities which are diffracted by the corners (i.e., loosely speaking, are not propagated along limits of transversely reflected rays) are smoother than the main singularities of the solution. More generally, we show that subject to a hypothesis of nonfocusing, diffracted wavefronts of any solution to the wave equation are smoother than the incident singularities. These results extend our previous work on edge manifolds to a situation where the fibers of the boundary fibration, obtained here by blowup of the corner in question, are themselves manifolds with corners.