Volume 29, 2023
|Number of page(s)||29|
|Published online||11 January 2023|
A free boundary problem in thermal insulation with a prescribed heat source
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli studi di Napoli Federico II,
Via Cintia, Complesso Universitario Monte S. Angelo,
2 Mathematical and Physical Sciences for Advanced Materials and Technologies, Scuola Superiore Meridionale, Largo San Marcellino 10, 80126 Napoli, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 30 November 2022
We study the thermal insulation of a bounded body Ω G ℝn, 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.
Mathematics Subject Classification: 35R35 / 35J25 / 35A01
Key words: Robin / thermal insulation / free boundary / heat source
© The authors. Published by EDP Sciences, SMAI 2023
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