Journal
APPLIED MATHEMATICAL MODELLING
Volume 40, Issue 1, Pages 115-125Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2015.05.006
Keywords
Lithium-ion batteries; Mathematical model; Partial differential equations; Boundary conditions; Uniqueness of solution; Existence of solution
Funding
- Spanish Ministry of Economy and Competitiveness [MTM2011-22658]
- research group MOMAT - Banco Santander [910480]
- Universidad Complutense de Madrid
- Junta de Andalucia
- European Regional Development Fund [P12-TIC301]
- OCIAM (University of Oxford)
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We discuss the well-posedness of a mathematical model that is used in the literature for the simulation of lithium-ion batteries. First, a mathematical model based on a macrohomogeneous approach is presented, following previous work. Then it is shown, from a physical and a mathematical point of view, that a boundary condition widely used in the literature is not correct. Although the errors could be just sign typos (which can be explained as carelessness in the use of d/dx versus d/dn, with n the outward unit vector) and authors using this model probably use the correct boundary condition when they solve it in order to do simulations, readers should be aware of the right choice. Therefore, the deduction of the correct boundary condition is done here, and a mathematical study of the well-posedness of the corresponding problem is presented. (C) 2015 Elsevier Inc. All rights reserved.
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