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September 2006 On the Well-posedness of a Mathematical Model for Lithium-Ion Battery Systems
Jinbiao Wu, Jinchao Xu, Henghui Zou
Methods Appl. Anal. 13(3): 275-298 (September 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 $t>0$.


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Jinbiao Wu. Jinchao Xu. Henghui Zou. "On the Well-posedness of a Mathematical Model for Lithium-Ion Battery Systems." Methods Appl. Anal. 13 (3) 275 - 298, September 2006.


Published: September 2006
First available in Project Euclid: 18 January 2008

zbMATH: 1135.35300
MathSciNet: MR2382436

Primary: 35G25 , 35G30 , 35J55 , 35J70 , 35K15 , 35K20 , 35M10

Keywords: a priori estimates , ‎fixed point theorems , Lithium-ion battery , Nash-Moser-DeGiorgi boot strap , Newton-Krylov-multigrid method

Rights: Copyright © 2006 International Press of Boston

Vol.13 • No. 3 • September 2006
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