| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 3 | |
| Number of page(s) | 29 | |
| DOI | https://doi.org/10.1051/cocv/2022081 | |
| Published online | 11 January 2023 | |
A free boundary problem in thermal insulation with a prescribed heat source
1
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli studi di Napoli Federico II,
Via Cintia, Complesso Universitario Monte S. Angelo,
80126
Napoli,
Italy
2
Mathematical and Physical Sciences for Advanced Materials and Technologies, Scuola Superiore Meridionale,
Largo San Marcellino 10,
80126
Napoli,
Italy
* Corresponding author: p.acampora98@gmail.com
Received:
30
June
2022
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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