On the well-posedness of a multiscale mathematical model for Lithium-ion batteries

TL;DR

This paper rigorously proves the well-posedness of the full nonlinear Newman model for Lithium-ion batteries, establishing existence of solutions both locally and globally in time under certain conditions.

Contribution

It provides the first proof of existence in time for the complete Newman model, extending previous simplified case results.

Findings

Proved local well-posedness of the model

Extended results to global in time under specific hypotheses

Established a rigorous mathematical framework for the model

Abstract

We consider the mathematical treatment of a system of nonlinear partial differential equations based on a model, proposed in 1972 by J. Newman, in which the coupling between the Lithium concentration, the phase potentials and temperature in the electrodes and the electrolyte of a Lithium battery cell is considered. After introducing some functional spaces well-adapted to our framework we obtain some rigorous results showing the well-posedness of the system, first for some short time and then, by considering some hypothesis on the nonlinearities, globally in time. As far as we know, this is the first result in the literature proving existence in time of the full Newman model, which follows previous results by the third author in 2016 regarding a simplified case.