论文标题
分析用于热传导流体混合物的Maxwell-Stefan系统
Analysis of Maxwell-Stefan systems for heat conducting fluid mixtures
论文作者
论文摘要
事实证明，麦克斯韦 - 斯特凡较弱方程的全球范围内存在以fick-osag-osager形式的形式存在。该模型由局部质量密度的质量平衡方程以及总能量的能量平衡方程组成。扩散和热通量线性地取决于热化学势和温度梯度的梯度，并包括soret和dufour效应。交叉扩散系统表现出熵结构，该结构源自热力学建模。扩散矩阵缺乏正定性是由于总质量密度在时间上恒定的事实得到了补偿。熵估计得出A.E.部分质量密度和温度的阳性。还认为扩散矩阵因消失的部分质量密度而退化。
The global-in-time existence of bounded weak solutions to the Maxwell-Stefan-Fourier equations in Fick-Onsager form is proved. The model consists of the mass balance equations for the partial mass densities and and the energy balance equation for the total energy. The diffusion and heat fluxes depend linearly on the gradients of the thermo-chemical potentials and the gradient of the temperature and include the Soret and Dufour effects. The cross-diffusion system exhibits an entropy structure, which originates from the thermodynamic modeling. The lack of positive definiteness of the diffusion matrix is compensated by the fact that the total mass density is constant in time. The entropy estimate yields the a.e. positivity of the partial mass densities and temperature. Also diffusion matrices are considered that degenerate for vanishing partial mass densities.
