”Heat flow problems across fractal layers”,

We consider a parabolic transmission problem involving a second order condition on a Koch-type fractal layer. This "unusual" boundary transmission condition (for both elliptic and parabolic problems) can be traced back to the so-called Ventsel problem studied in the late 1950s. From the physical point of view, these problems have been considered in connection of various applications. In the framework of heat propagation, they occur in the modeling of heat transfer across highly conductive thin layers. In this talk, existence, uniqueness and regularity results for the strict solution for both the fractal and the pre-fractal problems will be presented together with results on the convergence of the solutions of the pre-fractal problems. A priori error estimates for the numerical approximation of the solution of the pre-fractal transmission problems together with some numerical simulations will be discussed