论文标题
能源反应扩散系统的全球存在分析
Global existence analysis of energy-reaction-diffusion systems
论文作者
论文摘要
我们为热力学一致的反应 - （交叉）扩散系统建立了全球及时存在结果，该反应与描述传热的方程式结合在一起。我们的主要兴趣是建模依赖物种的扩散性，同时确保热力学一致性。非等温病例的一个关键难度在于交叉扩散类型现象（如soret和dufour效应）的内在存在：由于热力学平衡的温度/能量依赖性，非变化温度梯度也可能在恒定浓度的情况下驱动浓度范围；同样，即使在空间恒温的情况下，非变化浓度梯度也可能驱动热通量。我们使用时间离散和正则化技术，并根据适当的熵和相关的熵产生得出先验估计。在出现不可积分扩散通量或反应项的情况下，使用重量化的溶液。
We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretisation and regularisation techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalised solutions are used in cases where non-integrable diffusion fluxes or reaction terms appear.
