# Existence for a Cahn-Hilliard Model for Lithium-Ion Batteries with Exponential-Growth Boundary Conditions

Source: [Existence for a Cahn-Hilliard Model for Lithium-Ion Batteries with Exponential-Growth Boundary Conditions](<https://www.sota2.com/research/paper/68fa596a1e209131ce9b6be1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T15:53:14.626Z

Authors: Kerrek Stinson

Published: 2020-10-16T17:45:18.000Z

## Abstract

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 $\\partial\_\\nu \\mu = R(c,\\mu)$ for the chemical potential $\\mu$, with $c$, the lithium-ion density. Importantly, $R$ depends exponentially on $\\mu$. 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2010.08533>)

[PDF](<https://arxiv.org/pdf/2010.08533.pdf>)