半线性弹性动力学方程组余法奇性传播

数学物理学报 ›› 2009, Vol. 29 ›› Issue (6): 1743-1749.

半线性弹性动力学方程组余法奇性传播

四川理工学院理学院四川自贡 643000

收稿日期:2007-11-22 修回日期:2008-10-08 出版日期:2009-12-25 发布日期:2009-12-25
基金资助:
四川理工学院科研项目(2004ZR024)和四川理工学院理学院重点项目(09LXYA03)资助

Propagation of Conormal Singularities for Semilinear Elastic Dynamical System

School of Science, Sichuan University of Science and Engineering, Sichuan Zigong 643000

Received:2007-11-22 Revised:2008-10-08 Online:2009-12-25 Published:2009-12-25
Supported by:
四川理工学院科研项目(2004ZR024)和四川理工学院理学院重点项目(09LXYA03)资助

摘要/Abstract

摘要：

该文在余法分布理论框架下研究半线性弹性动力学方程组原点初值奇性的传播. 建立了适当的余法分布空间,利用方程组解的Stokes-Helmholtz分解方法, 讨论了余法分布空间中函数的分解性质; 如果初值函数在原点有适当余法奇性且L^∞有界, 通过构造解序列的方法证明初值问题存在仅在方程组特征面上有余法奇性,且正则性更高的唯一L^∞有界解.

关键词: 半线性弹性动力学方程组, 奇性传播, 余法分布空间, 函数分解, 模估计

Abstract:

The propagation of initial singularities for a semilinear elastic dynamic system is discussed. First, construct conormal distribution spaces for the system and discuss its character. Then study decomposition, as Stokes-Helmholtz decomposition in elastodynamics, of functions in the spaces. Lastly, prove, if initial dates are
bounded and have conormal singularities in zeros, then initial problems have bounded solutions with conormal
singularities only in two characteristic surfaces of the system, and have higher regularities.

Key words: Semilinear elastic dynamical system, Propagation of singularity, Conormal distribution space, Decomposition, Vector field, Pseudo-differential operator

中图分类号:

35G25

雷远明, 刘自山. 半线性弹性动力学方程组余法奇性传播[J]. 数学物理学报, 2009, 29(6): 1743-1749.

LEI Yuan-Ming, LIU Zi-Shan. Propagation of Conormal Singularities for Semilinear Elastic Dynamical System[J]. Acta mathematica scientia,Series A, 2009, 29(6): 1743-1749.

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