Journal
ADVANCES IN NONLINEAR ANALYSIS
Volume 8, Issue 1, Pages 1132-1157Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/anona-2018-0041
Keywords
Lithium-ion battery cell; multiscale mathematical model; Green operators; fixed point theory; Browder-Minty existence results; super and sub solutions
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Funding
- Spanish Ministry of Economy, Industry and Competitiveness [MTM2014-57113-P, MTM2015-64865-P]
- FPU Grant from the Ministerio de Educacion, Cultura y Deporte (Spain)
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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.
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