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arXiv · 2205.03275

A free boundary problem in thermal insulation with a prescribed heat source

Paolo Acampora·Emanuele Cristoforoni·Carlo Nitsch·Cristina Trombetti
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Abstract

We study the thermal insulation of a bounded body $Ω\subset\mathbb{R}^n$, under a prescribed heat source $f>0$, via a bulk layer of insulating material. We consider a model of heat transfer between the insulated body and the environment determined by convection; this corresponds to Robin boundary conditions on the free boundary of the layer. We show that a minimal configuration exists and that it satisfies uniform density estimates.

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Paolo Acampora, Emanuele Cristoforoni, Carlo Nitsch, Cristina Trombetti. 2022-10-14. A free boundary problem in thermal insulation with a prescribed heat source. https://doi.org/10.1051/cocv%2F2022081

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