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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 3: 743-759. doi: 10.3934/mbe.2013.10.743
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Calcium waves with mechano-chemical couplings

  • 1.
    Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw
  • 2.
    Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw
  • Received: 01 June 2012 Accepted: 29 June 2018 Published: 01 April 2013

  • MSC : Primary: 35K57, 35C07; Secondary: 35Q92.

  • As follows from experiments, waves ofcalcium concentration in biological tissuescan be easily excited by a local mechanical stimulation.Therefore the complete theory of calcium waves should alsotake into account couplingbetween mechanical and chemical processes.In this paper we consider the existenceof travelling waves for buffered systems, as in [22], completed, however,by an equation for mechanical equilibrium and respective mechanochemical coupling terms.Thus the considered, coupled system consists of reaction-diffusion equations (forthe calcium and buffers concentrations) and equations for thebalance of mechanical forces.

    Citation: Bogdan Kazmierczak, Zbigniew Peradzynski. Calcium waves with mechano-chemical couplings[J]. Mathematical Biosciences and Engineering, 2013, 10(3): 743-759. doi: 10.3934/mbe.2013.10.743

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  • As follows from experiments, waves ofcalcium concentration in biological tissuescan be easily excited by a local mechanical stimulation.Therefore the complete theory of calcium waves should alsotake into account couplingbetween mechanical and chemical processes.In this paper we consider the existenceof travelling waves for buffered systems, as in [22], completed, however,by an equation for mechanical equilibrium and respective mechanochemical coupling terms.Thus the considered, coupled system consists of reaction-diffusion equations (forthe calcium and buffers concentrations) and equations for thebalance of mechanical forces.


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