Existence of solution to a system of PDEs modelling the crystal growth inside lithium batteries

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Abstract
We study a model for lithium (Li) electrodeposition on Li-metal electrodes that leads to dendritic pattern formation. The model comprises of a system of three coupled PDEs, taking the form of an Allen–Cahn equation, a Nernst–Planck equation, and a Poisson equation. We prove the existence of a weak solution and stability results for this system and present numerical simulations resulting from a finite-element approximation of the system, which illustrate the dendritic nature of solutions to the model.