摘要
有一类重要的偏微分方程组称为Maxwell-Stefan反应交叉扩散方程组,其扩散矩阵的表达式一般十分复杂,所以要得到扩散矩阵的性质往往比较困难。鉴于此,首先对Maxwell-Stefan方程组的行列式计算进行的研究。方程组的扩散矩阵乘以某一个辅助矩阵之后是一个对角矩阵,由此推出扩散矩阵的行列式。然后证明Maxwell-Stefan方程组的扩散矩阵满足利普西茨条件。Maxwell-Stefan方程组的扩散矩阵的逆矩阵的形式比较简单且有规律性,所以利用扩散矩阵的逆矩阵来推出扩散矩阵的利普西茨性质是研究这一类方程组的重要手段和技巧。结果表明利普西茨性质是一种非常优良的性质,在证明微分方程组解的存在性与唯一性的过程当中可起着重要的作用。
The Maxwell-Stefan reaction-cross-diffusion system was an important system of partial differential equations.Its diffusion matrix had a very complicated form,so it was quite difficult to derive useful properties of the diffusion matrix.Firstly,the determinant of the diffusion matrix had been computed.The multiplication between the diffusion matrix and an auxiliary matrix is a diagonal one,and the determinant of the diffusion matrix can be derived.Secondly,the Lipschitz property for the diffusion matrix of the Maxwell-Stefan type system had been shown.The inverse of the diffusion matrix has a simple form,and the Lipschitz property of the diffusion matrix is shown by investigating its inverse.The results show that Lipschitz property plays a major role in proving the existence and uniqueness of a solution to a system of differential equations.
作者
林溪
LIN Xi(School of Arts and Sciences,Guangzhou Maritime University,Guangzhou Guangdong 510725,China)
出处
《广州航海学院学报》
2025年第3期73-77,共5页
Journal of Guangzhou Maritime University
