Existence of solution to a system of PDEs modeling the crystal growth inside lithium batteries
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| Format: | Preprint |
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2023
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| _version_ | 1866914204691202048 |
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| author | Lakkis, Omar Skouras, Alexandros Styles, Vanessa |
| author_facet | Lakkis, Omar Skouras, Alexandros Styles, Vanessa |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_16202 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Existence of solution to a system of PDEs modeling the crystal growth inside lithium batteries Lakkis, Omar Skouras, Alexandros Styles, Vanessa Analysis of PDEs Materials Science Numerical Analysis 35Q74, 35Q56 (primary), 35Q92, 78A57 (secondary) G.1.8; G.1.10; J.2 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. |
| title | Existence of solution to a system of PDEs modeling the crystal growth inside lithium batteries |
| topic | Analysis of PDEs Materials Science Numerical Analysis 35Q74, 35Q56 (primary), 35Q92, 78A57 (secondary) G.1.8; G.1.10; J.2 |
| url | https://arxiv.org/abs/2310.16202 |