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In this paper we study a system of partial differential equations whichmodels lithium-ion batteries. The system describes the conservation of Lithiumand conservation of charges in the solid and electrolyte phases, together withthe conservation of energy. The mathematical challenge is due to the fact thatthe reaction terms in the system involve the hyperbolic sine function alongwith possible degeneracy in one of the high order terms. We obtain a localexistence assertion for the initial boundary problem for the system whichoffers insight into how long a battery can last.

Life span of solutions to a PDE model for Lithium-ion batteries in high space dimensions