论文标题
具有指数增长边界条件的锂离子电池的Cahn-Hilliard模型的存在
Existence for a Cahn-Hilliard Model for Lithium-Ion Batteries with Exponential-Growth Boundary Conditions
论文作者
论文摘要
将Cahn-Hilliard反应模型（一种非线性，进化PDE）引入了锂离子电池中的模型相分离。使用Butler-Volmer动力学来进行电化学的一致性，该模型允许锂离子通过非线性robin型边界边界条件$ \partial_νμ= r（c，μ）$，用于$ c $，带有$ c $，lithium-ion密度。重要的是，$ r $呈指数级取决于$μ$。固定点方法用于获得Cahn-Hilliard反应模型的常规解决方案，$ 3，允许像物理应用一样恢复指数边界条件。
The Cahn-Hilliard reaction model, a nonlinear, evolutionary PDE, was introduced to model phase separation in lithium-ion batteries. Using Butler-Volmer kinetics for electrochemical consistency, this model allows lithium-ions to enter the domain via a nonlinear Robin-type boundary condition $\partial_νμ= R(c,μ)$ for the chemical potential $μ$, with $c$, the lithium-ion density. Importantly, $R$ depends exponentially on $μ$. Fixed point methods are applied to obtain existence of regular solutions of the Cahn-Hilliard reaction model in dimension $3,$ allowing for recovery of exponential boundary conditions as in the physical application.
