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arXiv · 2507.02451

A field-road system with a rectifiable set

Matthieu Bonnivard·Romain Ducasse·Antoine Lemenant·Alessandro Zilio
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Abstract

The aim of this paper is to define a field-road system in 2D where the road is a merely 1D-rectifiable set. For this purpose we introduce a general setting in order to define a parabolic problem onto a rectifiable set, which is coupled with another more classical parabolic problem outside this set, with transmission conditions.

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Matthieu Bonnivard, Romain Ducasse, Antoine Lemenant, Alessandro Zilio. 2025-07-03. A field-road system with a rectifiable set. https://arxiv.org/abs/2507.02451

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