Eigenvalue problems in fuel cell dynamics

An eigenvalue problem arising from the study of gas dynamics in a loaded tubular solid oxide fuel cell is considered. An asymptotic theory from which the equations are derived is reviewed, and the results of analysis on the small and large parameter asymptotics are presented. These results suggest an interesting and hitherto unknown property of a class of Sturm-Liouville problems in which the first eigenvalue approaches zero but subsequent ones approach infinity as a parameter approaches zero. This was first discovered numerically and later confirmed asymptotically and rigorously.