https://inria.hal.science/inria-00073504Henrot, AntoineAntoineHenrotSokolowski, JanJanSokolowskiNUMATH - Mathematical Analysis and Numerical Simulation of Non-Linear Models - INRIA Lorraine - Inria - Institut National de Recherche en Informatique et en AutomatiqueShape Optimization Problem for Heat EquationHAL CCSD1997shape optimizationradon measureshape derivativeparabolic equation[INFO.INFO-OH] Computer Science [cs]/Other [cs.OH]Inria, Rapport De Recherche2006-05-24 13:04:492023-02-07 03:39:592006-05-31 14:24:27enReportsapplication/pdf1In this paper the support of a Radon measure is selected in an optimal way. The solution of the parabolic equation depends on the mesure via the mixed type boundary conditions. The existence of a solution for a class of domain optimization problems is shown. We also investigate the behaviour of the optimal solution for some time $T$, when $T\to\infty$ and we prove that it converges to the optimal solution of the stationary problem. The first order necessary optimality conditions are derived.