English

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

Analysis of PDEs 2025-12-18 v3 Materials Science Numerical Analysis Numerical Analysis

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 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.

Keywords

Cite

@article{arxiv.2310.16202,
  title  = {Existence of solution to a system of PDEs modeling the crystal growth inside lithium batteries},
  author = {Omar Lakkis and Alexandros Skouras and Vanessa Styles},
  journal= {arXiv preprint arXiv:2310.16202},
  year   = {2025}
}

Comments

23 pages, 4 figures (25 pictures), free software and open source code available