JournalsifbVol. 28, No. 3pp. 447–462

A field-road system with a rectifiable set

  • Matthieu Bonnivard

    CNRS, INSA Lyon, Université Claude Bernard Lyon 1, Université Jean Monnet, ICJ UMR5208, Ecully, France

  • Romain Ducasse

    CNRS, Laboratoire Jacques-Louis Lions (LJLL), Paris, France

  • Antoine Lemenant

    UMR 7502 IECL, Vandoeuvre-lès-Nancy, France

  • Alessandro Zilio

    CNRS, Laboratoire Jacques-Louis Lions (LJLL), Paris, France
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Abstract

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

Cite this article

Matthieu Bonnivard, Romain Ducasse, Antoine Lemenant, Alessandro Zilio, A field-road system with a rectifiable set. Interfaces Free Bound. 28 (2026), no. 3, pp. 447–462

DOI 10.4171/IFB/551