数学物理学报
數學物理學報
수학물이학보
ACTA MATHEMATICA SCIENTIA
2009年
6期
1743-1749
,共7页
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.
半線性彈性動力學方程組%奇性傳播%餘法分佈空間%函數分解%模估計.
반선성탄성동역학방정조%기성전파%여법분포공간%함수분해%모고계.
Semilinear elastic dynamical system%Propagation of singularity%Conormal dis-tribution space%Decomposition%Vector field%Pseudo-differential operator.
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.
該文在餘法分佈理論框架下研究半線性彈性動力學方程組原點初值奇性的傳播.建立瞭適噹的餘法分佈空間,利用方程組解的Stokes-Helmholtz分解方法,討論瞭餘法分佈空間中函數的分解性質;如果初值函數在原點有適噹餘法奇性且L~∞有界,通過構造解序列的方法證明初值問題存在僅在方程組特徵麵上有餘法奇性,且正則性更高的唯一L~∞有界解.
해문재여법분포이론광가하연구반선성탄성동역학방정조원점초치기성적전파.건립료괄당적여법분포공간,이용방정조해적Stokes-Helmholtz분해방법,토론료여법분포공간중함수적분해성질;여과초치함수재원점유괄당여법기성차L~∞유계,통과구조해서렬적방법증명초치문제존재부재방정조특정면상유여법기성,차정칙성경고적유일L~∞유계해.
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.
