A field-road system with a rectifiable set
Matthieu Bonnivard (ECL, ICJ, MMCS), Romain Ducasse (LJLL (UMR\_7598), UPCit\'e), Antoine Lemenant (IECL), Alessandro Zilio (LJLL (UMR\_7598), UPCit\'e)
TL;DR
This paper introduces a mathematical framework for modeling a 2D field-road system where the road is represented as a 1D-rectifiable set, coupling parabolic problems inside and outside the set with transmission conditions.
Contribution
It develops a general setting to define and analyze parabolic problems on rectifiable sets coupled with classical problems outside, advancing the mathematical modeling of field-road systems.
Findings
Established a mathematical model for field-road systems with rectifiable roads.
Defined transmission conditions coupling interior and exterior parabolic problems.
Provided a framework for analyzing PDEs on rectifiable sets in 2D.
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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