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Gholam-Ali Zakeri 《Applied mathematics and computation》2010,217(2):830-4889
We provide a rigorous analysis of structure of a ray tube in geometrical shock dynamics. Our aim is to shed more lights on the cross-sectional area function of a ray tube. We have shown that for a given ray tube and a given initial value of cross-sectional area, then its cross-sectional area can be determined uniquely everywhere. We give a definition of cross-sectional area of a ray tube in precise mathematical terms and from that we derive a set of relations, each describing the cross-sectional area for an arbitrary ray tube in geometrical shock dynamics. We have shown that from our results one can deduce Whitham’s area function relation as a partial differential equation from our general formulations. Some applications are discussed. 相似文献
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沈玉良 《数学年刊A辑(中文版)》2003,(2)
讨论了在实值调和函数所组成的Dirichlet空间上由拟对称同胚给出的拉回算子,并回答Schober(见[15])关于一些区域泛函的有关问题. 相似文献
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