A field-road system with a rectifiable set

2025/07/03 by Bonnivard, Matthieu, Ducasse, Romain, Lemenant, Antoine +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.02451

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.

Citations

• Optimal reinforcing networks for elastic membranes
• On a phase field approximation of the planar Steiner problem: existence, regularity, and asymptotic of minimizers
• The influence of a line with fast diffusion on Fisher-KPP propagation
• Energies with respect to a measure and applications to low dimensional structures

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