Life span of solutions to a PDE model for Lithium-ion batteries in high space dimensions

TL;DR

This paper analyzes a PDE model for lithium-ion batteries, addressing the mathematical challenges of reaction terms and degeneracy to determine the lifespan of battery solutions.

Contribution

It establishes a local existence result for the PDE system modeling lithium-ion batteries, providing insights into battery longevity.

Findings

Proves local existence of solutions to the PDE system

Handles reaction terms involving hyperbolic sine functions

Provides insights into battery lifespan based on PDE analysis

Abstract

In this paper we study a system of partial differential equations which models lithium-ion batteries. The system describes the conservation of Lithium and conservation of charges in the solid and electrolyte phases, together with the conservation of energy. The mathematical challenge is due to the fact that the reaction terms in the system involve the hyperbolic sine function along with possible degeneracy in one of the high order terms. We obtain a local existence assertion for the initial boundary problem for the system which offers insight into how long a battery can last.