An uncoupled limit model for a high-contrast problem in a thin multi-structure

We investigate a degenerating elliptic problem in multi-structure $\Omega\_\varepsilon$ of $\mathbb{R}^3$, the framework thermal stationary conduction with highly contrasting diffusivity. Precisely, consists fixed basis $\Omega^-$ surmounted by thin cylinder $\Omega\_\varepsilon^+$ height $1$ and cross-section small diameter order $\varepsilon$. Moreover, $\Omega^+\varepsilon$ contains cylindrical core, always $\varepsilon$, conductivity $1$, surrounded ring $\varepsilon^2$. Also has By assuming that temperature is zero on top bottom boundary $\Omega\varepsilon$, while flux remaining part boundary, under suitable choice source term we prove limit problem, as $\varepsilon$ vanishes, boils down to two uncoupled problems: one $\Omega^+\_1$, $\Omega^+\_1$ nonlocal. corrector result obtained.