Persistence of zero velocity fronts in reaction diffusion systems

Steady, nonpropagating, fronts in reaction diffusion systems usually exist only for special sets of control parameters. When varying one control param eter, the front velocity may become zero only at isolated values (where the Maxwell condition is satisfied, for potential systems). The experimental o bservation of fronts with a zero velocity over a finite interval of paramet ers, e.g., in catalytic experiments [Barelko , Chem. Eng. Sci., 33, 805 (19 78)], therefore, seems paradoxical. We show that the velocity dependence on the control parameter may be such that velocity is very small over a finit e interval, and much larger outside. This happens in a class of reaction di ffusion systems with two components, with the extra assumptions that (i) th e two diffusion coefficients are very different, and that (ii) the slowly d iffusing variables has two stable states over a control parameter range. Th e ratio of the two velocity scales vanishes when the smallest diffusion coe fficient goes to zero. A complete study of the effect is carried out in a m odel of catalytic reaction. (C) 2000 American Institute of Physics. [S1054- 1500(00)01903-0].