On the Well-posedness of a Mathematical Model for Lithium-Ion Battery Systems
Jinbiao Wu, Jinchao Xu, Henghui Zou · Methods and Applications of Analysis · 2006
In this paper, we shall establish the well-posedness of a mathematical model for a special class of electrochemical power device -lithium-ion battery.The underlying partial differential equations in the model involve a (mix and fully) coupled system of quasi-linear elliptic and parabolic equations.By exploring some special structure, we are able to adopt the well-known Nash-Moser-DeGiorgi boot strap to establish suitable a priori supremum estimates for the electric potentials.Using the supremum estimates, we apply the Leray-Schauder theory to establish the existence and uniqueness of a subsystem of elliptic equations that describe the electric potentials in the model.We then employ a Schauder fix point theorem to obtain the local (in time) existence for the whole model.We also consider the global existence of a modified 1-d governing system under additional assumptions.In particular, we are able to derive uniform a priori estimates depending only on the existence time T , including the supremum estimates for electric potentials and growth and decay estimates for the concentration c.Using the uniform estimates, we prove that the modified system has a solution for all time t > 0.