Journal of Mathematical Biology

, Volume 62, Issue 1, pp 1–38 | Cite as

Calcium waves with fast buffers and mechanical effects

  • Bogdan Kaźmierczak
  • Zbigniew Peradzyński


In the paper we consider the existence of calcium travelling waves for systems with fast buffers. We prove the convergence of the travelling waves to an asymptotic limit as the kinetic coefficients characterizing the interaction between calcium and buffers tend to infinity. To be more precise, we prove the convergence of the speeds as well as the calcium component concentration profile to the profile of the travelling wave of the reduced equation. Additionally, we take into account the effect of coupling between the mechanical and chemical processes and show the existence as well the monotonicity of the profiles of concentrations. This property guarantees their positivity.


Calcium waves Reaction–diffusion systems Mechanochemical coupling 


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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland
  2. 2.Institute of Applied Mathematics and MechanicsWarsaw UniversityWarsawPoland

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