Mechanical effects coupled with calcium waves

where θ = ∇ · u is the dilation and u is the displacement. The stress tensor σ ≡ σij , where (1.3) σij = θλδij + 2Gǫij + ν1θ,tδij + ν2ǫij,t + τij . In Eq. (1.1), c denotes the free cytosolic calcium concentration, D is its effective diffusion coefficient, f(c) is the function describing calcium transport into and out of the cytosol. In Eq. (1.3), ǫij are the components of the deformation tensor ǫ = 1/2(∇u +∇uT ), λ and G are the Lamé coefficients, whereas ν1 and ν2 are the viscosity coefficients. τij are the components of the so-called active traction tensor τ (resulting from the actin-myosin interaction). Below, we assume that τ is a diagonal tensor of the form τ = diag(τ11, τ22, τ33).