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