| 三维拟线性热弹性力学方程区域内部解的奇性传播规律 |
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| 引用本文： | 杨林,王亚光.三维拟线性热弹性力学方程区域内部解的奇性传播规律[J].数学年刊A辑(中文版),2005(3). |
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| 作者姓名： | 杨林 王亚光 |
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| 作者单位： | 湖南大学应用数学系，上海交通大学数学系 长沙 410082，上海 200240 |
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| 基金项目： | 国家自然科学基金(No．10131050)资助的项目． |
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| 摘 要： | 本文利用频率分析对角化的方法,研究了三维拟线性热弹性力学方程区域内部解的奇性传播规律. 首先从微局部观点出发,利用仿微分算子和拟微分算子将方程仿线性化和对角化.然后,利用穿梭法和经典的双曲方程和抛物方程理论,证明了区域内部解的奇性传播也是沿耦合方程组的双曲算子的零次特征带传播,并且当初值的奇性沿方程组的双曲算子的前向光锥传播时,时间t也具有很好的正则性.
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| 关 键 词： | 微局部分析 仿微分算子 双曲抛物耦合方程组 区域内部 |
PROPAGATION OF SINGULARITIES IN INTERIOR DOMAINS FOR QUASILINEAR THERMOELASTIC SYSTEMS IN THREE SPACE VARIABLES |
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| YANG Lin WANG Yaguang.PROPAGATION OF SINGULARITIES IN INTERIOR DOMAINS FOR QUASILINEAR THERMOELASTIC SYSTEMS IN THREE SPACE VARIABLES[J].Chinese Annals of Mathematics,2005(3). |
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| Authors: | YANG Lin WANG Yaguang |
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| Institution: | YANG Lin WANG Yaguang Department of Applied Mathematics,Hunan University,Changsha 410082,China. Department of Mathematics,Shanghai Jiao Tong University,Shanghai 200240,China. |
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| Abstract: | By using the diagonalization method of frequency analysis, propagation of singularities in interior domains for a quasilinear thermoelastic system in three space variables is investigated. First, by using paradifferential and quasidifferential operators, the quasilinear thermoelastic system is microlocally paralinearized and diagonalized. Second, by using the classical bootstrap argument and theories of hyperbolic and parabolic equations, it is proved that singularity in interior domains for the quasilinear thermoelastic system is propagated along a null bicharacteristic of the hyperbolic operator of the coupled system. Meanwhile, the authors also obtain that the time t can have a good regularity as the singularity of the initial data is propagated along the forward light conic of the hyperbolic operator. |
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| Keywords: | Microlocal analysis Paradifferential operators Hyperbolic-parabolic coupled systems Interior domains |
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