Sneyd, James; Dale, Paul D.; Duffy, Alastair Traveling waves in buffered systems: Applications to calcium waves. (English) Zbl 0916.35052 SIAM J. Appl. Math. 58, No. 4, 1178-1192 (1998). The authors study travelling waves for the reaction-diffusion model describing the concentration \(c\) of free cytosolic calcium which is heavily buffered. The model, which is related to the FitzHugh-Nagumo system, can be written as follows: \[ \Biggl(1+{b_t k^-k^+\over (k^-+ ck^+)^2}\Biggr) {\partial c\over\partial t}= \Biggl({\partial\over \partial x}\Biggr)^2 \Biggl(D_cc- D_b{b_t k^-\over k^-+ ck^+}\Biggr)+ f(c). \] \(D_c\), \(D_b\) are the diffusion coefficients of \(Ca^{2+}\) respectively the buffer \(B\), \(b_t\) is the total amount of \(B\) and \(k^+\), \(k^-\) are respectively the reaction constants for \(Ca^{2+}+ B\to CaB\) and its reverse. The function \(f\) is the usual \(f(c)= c(1- c)(c- a)\) with \(a\in \left(0,{1\over 2}\right)\). They show that travelling waves exist for \(D_b\) small and derive an approximate expression for the wave speed. They also give some numerical evidence. Finally, they show how experimental data may be used to distinguish between models. Reviewer: G.H.Sweers (Delft) Cited in 1 ReviewCited in 19 Documents MSC: 35K57 Reaction-diffusion equations 92C05 Biophysics Keywords:bistable equation; FitzHugh-Nagumo equations; excitable systems; approximate expression for the wave speed PDFBibTeX XMLCite \textit{J. Sneyd} et al., SIAM J. Appl. Math. 58, No. 4, 1178--1192 (1998; Zbl 0916.35052) Full Text: DOI