Diffusive boundary layers in the free-surface excitable medium spiral

Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in time scale between fast excitation and slow recovery, one can reduce the spiral problem to one involving the motion of a free surface separating the excited and quiescent phases. In this work, we study the free-surface problem in the limit of small diffusivity for the slow field variable. Specifically, we show that a previously found spiral solution in the diffusionless limit can be extended to finite diffusivity, without significant alteration. This extension involves the creation of a variety of boundary layers which cure all the undesirable singularities of the aforementioned solution. The implications of our results for the study of spiral stability are briefly discussed.