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

Advances in Nonlinear Analysis

article

J. Ildefonso Díaz¹  David Gómez-Castro¹  Angel M. Ramos¹ 

[1] Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid;Department of Applied Mathematics and Mathematical Analysis, Universidad Complutense de Madrid;Universidad Pontificia Comillas

关键词: Lithium-ion battery cell;    multiscale mathematical model;    Green operators;    fixed point theory;    Browder–Minty existence results;    super and sub solutions;   

DOI  :  10.1515/anona-2018-0041

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY