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On the well-posedness of a mathematical model for lithium-ion batteries.

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Ramos del Olmo, Ángel Manuel (2016) On the well-posedness of a mathematical model for lithium-ion batteries. Applied Mathematical Modelling, 40 (1). pp. 115-125. ISSN 0307-904X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0307904X15003546


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Boundary conditions; Existence of solution; Lithium-ion batteries; Mathematical model; Partial differential equations; Uniqueness of solution
Subjects:Sciences > Mathematics > Combinatorial analysis
ID Code:37813
Deposited On:23 May 2016 14:04
Last Modified:12 Dec 2018 15:06

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