This paper concerns the periodic homogenization of the stationary heat equation in a domain with two connected components, separated by an oscillating interface defined on prefractal Koch type curves. The problem depends both on the parameter ε that defines the periodic structure of the interface and on n, which is the index of the prefractal iteration. First, we study the limit as ε vanishes, showing that the homogenized problem is strictly dependent on the amplitude of the oscillations and the parameter appearing in the transmission condition. Finally, we perform the asymptotic behaviour as n goes to infinity, giving rise to a limit problem defined on a domain with fractal interface.
On the effective interfacial resistance through quasi-filling fractal layers / Capitanelli, Raffaela; Pocci, Cristina. - In: CHAOS, SOLITONS AND FRACTALS. - ISSN 0960-0779. - 105:(2017), pp. 43-50. [10.1016/j.chaos.2017.09.036]
On the effective interfacial resistance through quasi-filling fractal layers
CAPITANELLI, Raffaela;POCCI, CRISTINA
2017
Abstract
This paper concerns the periodic homogenization of the stationary heat equation in a domain with two connected components, separated by an oscillating interface defined on prefractal Koch type curves. The problem depends both on the parameter ε that defines the periodic structure of the interface and on n, which is the index of the prefractal iteration. First, we study the limit as ε vanishes, showing that the homogenized problem is strictly dependent on the amplitude of the oscillations and the parameter appearing in the transmission condition. Finally, we perform the asymptotic behaviour as n goes to infinity, giving rise to a limit problem defined on a domain with fractal interface.File | Dimensione | Formato | |
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