On the existence and approximation of optimal insulation layers

par Paolo Acampora

lundi 22 avr. 2024, 10:00 → 11:00 Europe/Paris

1016 (Université Paris-Cité (campus Grands Moulins))

We are interested in the thermal insulation of a body $\mathrm{\Omega }$ surrounded by a bulk layer $\mathrm{\Sigma }$ of insulating material. We consider a Robin boundary condition on the boundary of $\mathrm{\Sigma }$ that does not touch $\mathrm{\Omega }$; this corresponds to a model of heat transfer between the insulated body and the environment determined by convection. We will address the problem of proving the existence of an optimal $\mathrm{\Sigma }$, and we will study a way to approximate the problem via first-order asymptotic development by $\mathrm{\Gamma }$-convergence.