Spiral Wave Solutions for Reaction-Diffusion Equations in a Fast Reaction/Slow Diffusion Limit
A two species reaction-diffusion equation is studied in a distinguished limit of fast reaction and slow diffusion. Asymptotic matching yields a spiral solution whose rotation frequency is a unique function of the physical parameters and the constant pitch of the spiral. Using an idea of Fife the problem is first reduced to a free boundary problem. The solution is obtained by matching the core, where diffusion balances the curvature of the free boundary, to the far field where the effects of diffusion are small. The equations of motion are averaged over the rotation frequency to yield steady equations in the two regions. Helically symmetric solutions to the averaged equation reduce to solving a fourth-order ODE in the core region matched to a second-order ODE in the far field. Speculations on the dynamics of the system and coupling between the core and far field are presented.
© 1991 Elsevier Ltd.
Andrew J. Bernoff, Spiral wave solutions for reaction-diffusion equations in a fast reaction/slow diffusion limit, Physica D: Nonlinear Phenomena, Volume 53, Issue 1, October 1991, Pages 125-150, ISSN 0167-2789, 10.1016/0167-2789(91)90168-9. (http://www.sciencedirect.com/science/article/pii/0167278991901689)