On the effective interfacial resistance through quasi-filling fractal layers

Raffaela Capitanelli and Cristina Pocci

Chaos, Solitons & Fractals, 2017, vol. 105, issue C, 43-50

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.

Keywords: Homogenization; Prefractals and fractals; Elliptic operators; Asymptotics; Oscillating interface; Stationary heat equation (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:105:y:2017:i:c:p:43-50

DOI: 10.1016/j.chaos.2017.09.036

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