Homogenized model of reaction-diffusion in a porous medium

  title={Homogenized model of reaction-diffusion in a porous medium},
  author={Leonid Pankratov and Andrey Piatnitskii and Volodymyr Rybalko},
Abstract We study the initial boundary value problem for the reaction–diffusion equation, ∂ t u e −∇·(a e ∇u e )+g(u e )=h e in a bounded domain Ω with periodic microstructure F (e) ∪ M (e) , where a e ( x ) is of order 1 in F (e) and κ ( e ) in M (e) with κ ( e )→0 as e →0. Combining the method of two-scale convergence and the variational homogenization we obtain effective models which depend on the parameter θ =lim e →0 κ ( e )/ e 2 . In the case of strictly positive finite θ the effective… CONTINUE READING