The life-cycle of electric batteries depends on a complex system of interacting electrochemical and growth phenomena that produce dendritic structures during the discharge cycle. We study herein a system of 3 partial differential equations combining an Allen--Cahn phase-field model (simulating the dendrite-electrolyte interface) with the Poisson--Nernst--Planck systems simulating the electrodynamics and leading to the formation of such dendritic structures. We prove novel existence, uniqueness and stability results for this system and use it to produce simulations based on a finite element code.

翻译：电动汽车电池的寿命取决于放电循环过程中产生枝晶结构的复杂电化学与生长现象相互作用系统。本文研究了一个由三个偏微分方程组成的系统,该方程将Allen-Cahn相场模型(模拟枝晶-电解质界面)与模拟电动力学并导致枝晶结构形成的Poisson-Nernst-Planck系统相结合。我们证明了该系统新的存在性、唯一性和稳定性结果,并基于有限元代码进行了数值模拟。