Mathematical aspects of catalyst positioning in lithium/air batteries

In this paper we investigate a system of partial differential equations describing the clogging process of non-aqueous lithium/air batteries. The main aim is to optimize the positioning of catalysts on the surface of the pore of the battery in order to maximize the efficiency of the battery. To this end we analyze the parameter-to-state map which maps the initial catalyst positions cat0(x) to the diminishing radius of the pore until clogging. We obtain results on the continuity and Fréchet differentiability of the parameter-to-state map and we obtain the related sensitivity system. The paper also includes numerical experiments, which compare a greedy approach to catalyst positioning with results obtained by an analytic optimisation procedure.