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Necessary conditions for local and global existence to a reaction-diffusion system with fractional derivatives.

Haouam, Kamel; Sfaxi, Mourad — 2006

International Journal of Mathematics and Mathematical Sciences

Correctors for Parabolic Equations in a Heterogeneous Fibered Medium

Mourad Sfaxi; Ali Sili — 2007

Bollettino dell'Unione Matematica Italiana

We study the problem of correctors in the framework of the homogenization of linear parabolic equations posed in a heterogeneous medium $\Omega$ made of two materials. The first one is located in a set $F_{\epsilon}$ of cylindrical parallel fibers periodically distributed with a period of size $\epsilon$ , and the second one is located in the "matrix" $M_{\epsilon}=\Omega\setminus F_{\epsilon}$ . The ratio between the conductivity coefficients of the two materials is of order $1/\epsilon^{2}$ . After writing the homogenized problem, we give a corrector result and prove that the solution...

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