Stationary sets for the wave equation in crystallographic domains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Stationary sets for the wave equation in crystallographic domains

Authors:	Mark L Agranovsky Eric Todd Quinto

Affiliation:	Bar Ilan University, Ramat Gan, Israel ; Tufts University, Medford, Massachusetts

Abstract:	Let be a crystallographic group in $\mathbb R^n$ generated by reflections and let $\Omega$ be the fundamental domain of We characterize stationary sets for the wave equation in $\Omega$ when the initial data is supported in the interior of $\Omega.$ The stationary sets are the sets of time-invariant zeros of nontrivial solutions that are identically zero at . We show that, for these initial data, the -dimensional part of the stationary sets consists of hyperplanes that are mirrors of a crystallographic group $\tilde W$ , $W<\tilde W.$ This part comes from a corresponding odd symmetry of the initial data. In physical language, the result is that if the initial source is localized strictly inside of the crystalline $\Omega$ , then unmovable interference hypersurfaces can only be faces of a crystalline substructure of the original one.

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