| 半线性弹性动力学方程组余法奇性传播 |
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| 引用本文： | 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(A辑),2009,29(6):1743-1749. |
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| 作者姓名： | 雷远明 刘自山 |
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| 作者单位： | 四川理工学院理学院,四川,自贡,643000 |
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| 基金项目： | 四川理工学院科研项目，四川理工学院理学院重点项目 |
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| 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.
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| 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 |
| 收稿时间： | 2007-11-22 |
| 修稿时间： | 2008-10-08 |
Propagation of Conormal Singularities for Semilinear Elastic Dynamical System |
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| Institution: | School of Science, Sichuan University of Science and Engineering, Sichuan Zigong 643000 |
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| 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. |
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| Keywords: | Semilinear elastic dynamical system Propagation of singularity Conormal dis-tribution space Decomposition Vector field Pseudo-differential operator |
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