论文标题
关于燃料电池问题的良好性
On the wellposedness for a fuel cell problem
论文作者
论文摘要
本文研究了在相邻域中两个椭圆方程问题集的解决方案，海狸分别在普通界面上规定了海狸 - 夫妇和正规管教 - 沃尔默边界条件，分别是多孔 - 流体和膜。 Mathematically, the modeling tool is the coupled Stokes/Darcy problem, which consists of the Stokes equation on one part of the domain coupled to the Darcy equation, where the flow velocities are small and mainly driven by the pressure gradient in porous medium, completed by the thermoelectrochemical (TEC) system, which consists of the energy equation and the mass transport associated with electrochemical reactions, where the通用傅立叶，给欧姆法律的通量是通过在多维域中包括dufour-soret和peltier（seebeck cross效应）来给出的。目前的模型包括用于氢和甲醇跨界的大型模型。提出的模型中的新颖性在于焦耳效应在Stokes/darcy-Tec系统中的存在，完全通过温度依赖性（例如粘度和扩散系数）依赖于跨效率的浓度依赖于跨粘液和扩散系数的体温依赖于跨效率的浓度依赖性，并通过压力依赖性的浓度依赖性。本工作的目的是得出解决方案的定量估计值，以明确的数据条件。我们根据近似解决方案的定量估计来使用固定点和紧凑性参数。
This paper investigates the existence of weak solutions to two problems set of elliptic equations in adjoining domains, with Beavers--Joseph--Saffman and regularized Butler--Volmer boundary conditions being prescribed on the common interfaces, porous-fluid and membrane, respectively. Mathematically, the modeling tool is the coupled Stokes/Darcy problem, which consists of the Stokes equation on one part of the domain coupled to the Darcy equation, where the flow velocities are small and mainly driven by the pressure gradient in porous medium, completed by the thermoelectrochemical (TEC) system, which consists of the energy equation and the mass transport associated with electrochemical reactions, where the fluxes are given by generalized Fourier, Fick and Ohm laws, by including the Dufour--Soret and Peltier--Seebeck cross effects, in the multidimensional domain. The present model includes macrohomogeneous models for both hydrogen and methanol crossover. The novelty in the presented model lies in the presence of the Joule effect into the Stokes/Darcy-TEC system altogether to the quasilinear character given by temperature dependence of the physical parameters such as the viscosities and the diffusion coefficients, by the concentration-temperature dependence of cross-effects coefficients, and by the pressure dependence of the permeability. The purpose of the present work is to derive quantitative estimates for solutions to explicit smallness conditions on the data. We use fixed point and compactness arguments based on the quantitative estimates of approximated solutions.
