A hyperbolic problem with non-local constraint describing ion-rearrangement in a model for ion-lithium batteries

TL;DR

This paper analyzes a hyperbolic PDE with non-local constraints modeling ion rearrangement in lithium batteries, proving well-posedness, stability, and uniqueness in slow reaction regimes with entropic effects.

Contribution

It introduces a novel hyperbolic PDE model with non-local constraints for ion-lithium batteries and establishes key mathematical properties like well-posedness and stability.

Findings

Proved global well-posedness of the model

Established stability under certain regularity assumptions

Proved uniqueness under additional conditions

Abstract

In this paper we study the Fokker-Plank equation arising in a model which describes the charge and discharge process of ion-lithium batteries. In particular we focus our attention on slow reaction regimes with non-negligible entropic effects, which triggers the mass-splitting transition. At first we prove that the problem is globally well-posed. After that we prove a stability result under some hypothesis of improved regularity and a uniqueness result for the stability under some additional condition of