论文标题
热力学一致的减少铁腐蚀模型的数学分析
Mathematical analysis of a thermodynamically consistent reduced model for iron corrosion
论文作者
论文摘要
我们对铁的腐蚀模型感兴趣，其中铁阳离子和电子在固定的氧化物层中进化，受到自洽静电电位的影响。借助巴特勒 - 沃尔默公式，对边界的反应进行了建模，而静电电势模型电容器的边界条件位于材料之间界面上的静电电势电容器。我们的模型在现有论文中具有灵感，我们为其带来了轻微的修改，以使其与热力学及其第二个原则一致。基于自由能量估算，我们建立了解决问题的解决方案的全球存在，而无需对物理参数进行任何限制，这与以前的工作相反。该证明进一步依赖于均匀的估计值，这些化学势得益于摩擦迭代。最终提供了数值插图，以突出我们的新模型与先前研究的模型之间的相似性和差异。
We are interested in a reduced model for corrosion of iron, in which ferric cations and electrons evolve in a fixed oxide layer subject to a self-consistent electrostatic potential. Reactions at the boundaries are modeled thanks to Butler-Volmer formulas, whereas the boundary conditions on the electrostatic potential model capacitors located at the interfaces between the materials. Our model takes inspiration in existing papers, to which we bring slight modifications in order to make it consistent with thermodynamics and its second principle. Building on a free energy estimate, we establish the global in time existence of a solution to the problem without any restriction on the physical parameters, in opposition to previous works. The proof further relies on uniform estimates on the chemical potentials that are obtained thanks to Moser iterations. Numerical illustrations are finally provided to highlight the similarities and the differences between our new model and the one previously studied in the literature.
