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Traveling waves in buffered systems: Applications to calcium waves. (English) Zbl 0916.35052

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)

MSC:

35K57 Reaction-diffusion equations
92C05 Biophysics
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