非等温多孔介质中具有交叉扩散的Richard方程
Nonisothermal Richards flow in porous media with cross diffusion
AI总结：
本文研究了非等温多孔介质中两相流的弱熵解存在性，考虑了温度梯度和交叉扩散效应，并通过变分方法和紧致性理论推导先验估计。
摘要：
本文证明了非等温不可混溶可压缩两相非饱和流模型在多孔介质中大数据弱熵解的存在性。该模型具有热力学一致性，包含温度梯度和交叉扩散效应。由于总能量平衡中的一些项在经典弱意义下不可积，我们考虑所谓的变分熵解。通过熵平衡和总能量平衡推导出先验估计。利用Div-Curl引理实现紧致性。
英文摘要：
The existence of large-data weak entropy solutions to a nonisothermal immiscible compressible two-phase unsaturated flow model in porous media is proved. The model is thermodynamically consistent and includes temperature gradients and cross-diffusion effects. Due to the fact that some terms from the total energy balance are non-integrable in the classical weak sense, we consider so-called variational entropy solutions. A priori estimates are derived from the entropy balance and the total energy balance. The compactness is achieved by using the Div-Curl lemma.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
