## Efficient electrochemical model for lithium-ion cells. (arXiv:1709.03970v1 [math.AP])

Lithium-ion batteries are used to store energy in electric vehicles. Physical
models based on electro-chemistry accurately predict the cell dynamics, in
particular the state of charge. However, these models are nonlinear partial
differential equations coupled to algebraic equations, and they are
computationally intensive. Furthermore, a variable solid-state diffusivity
model is recommended for cells with a lithium ion phosphate positive electrode
to provide more accuracy. This variable structure adds more complexities to the
model. However, a low-order model is required to represent the lithium-ion
cells' dynamics for real-time applications. In this paper, a simplification of
the electrochemical equations with variable solid-state diffusivity that
preserves the key cells' dynamics is derived. The simplified model is
transformed into a numerically efficient fully dynamical form. It is proved
that the simplified model is well-posed and can be approximated by a low-order
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