严格双曲型PDE波阵面抛物奇点处的局部Petrovskii空泡
Local Petrovskii lacunas at parabolic singular points of wavefronts of strictly hyperbolic PDE's
摘要：
我们列举了当地的Petrovskii缺陷（即，当地的正则性的主要基本解的领域）的严格双曲型PDE的常系数$R^N$在其波前的抛物奇点。这些点形成了下一个困难的家庭类的自然分类的奇点后，所谓的简单奇点，以前研究。此外，我们提出了一个计算机程序计数的拓扑不同morsification的临界点的光滑函数，因此也为本地组件的补充，一个通用的波前在其奇点。
英文摘要：
We enumerate the local Petrovskii lacunas (that is, the domains of local regularity of the principal fundamental solutions) of strictly hyperbolic PDE's with constant coefficients in $R^N$ at the parabolic singular points of their wavefronts. These points form the next difficult family of classes of the natural classification of singular points after the so-called simple singularities, studied previously. Also we promote a computer program counting for topologically different morsifications of critical points of smooth functions, and hence also for local components of the complement of a generic wavefront at its singular points.
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