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Spectral stability of post-fertilization traveling waves
Gilberto Flores and Ramón G. Plaza
This paper studies the stability of a family of post-fertilization traveling waves on eggs proposed by Lane et. al, consisting of an elastic deformation pulse on the egg's surface, and a calcium concentration profile. The family is indexed by a coupling parameter $\epsilon > 0$ that measures the contraction stress effects on the egg's surface. It is shown that the corresponding family of Evans functions for $\epsilon>0$ converges uniformly to the non-vanishing Evans function of the decoupled waves when $\epsilon = 0$, proving spectral stability.