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Stability of Reaction-Diffusion Fronts
Ziqiang Zhang and S. A. E. G. Falle
Proceedings: Mathematical and Physical Sciences
Vol. 446, No. 1928 (Sep. 8, 1994), pp. 517-528
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52476
Page Count: 12
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Horvath, Petrov, Scott and Showalter (1993) have shown that isothermal reaction-diffusion fronts with cubic autocalysis are linearly unstable to two-dimensional disturbances if the ratio, δ , of the diffusion coefficient of the reactant to that of the autocatalyst, is sufficiently large. However, they were only able to obtain an analytic expression for the growth rate by assuming an infinitely thin reaction zone, which is a poor approximation for cubic autocatalysis. We have carried out a linear stability analysis of such fronts with a finite reaction rate, and find that the critical δ for instability is unchanged, but the range of unstable wavenumbers is larger and increases rather than decreases with δ .
Proceedings: Mathematical and Physical Sciences © 1994 Royal Society