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

In this paper we study a system of partial differential equations which models lithiumion batteries.The system describes the conservation of Lithium and conservation of charges in the solid and electrolyte phases, together with the conservation of energy.The mathematical challenge is due to the fact that the reaction terms in the system involve the hyperbolic sine function along with possible degeneracy in one of the high order terms.We obtain a local existence assertion for the initial boundary problem for the system.In particular, a lower bound for the blow-up time can be derived from our result.We hope that our analysis can lead to a deeper understanding of battery life.