%0 Report %T Shape Optimization Problem for Heat Equation %+ Mathematical Analysis and Numerical Simulation of Non-Linear Models (NUMATH) %A Henrot, Antoine %A Sokolowski, Jan %N RR-3185 %P 23 %I INRIA %8 1997 %D 1997 %K shape optimization %K radon measure %K shape derivative %K parabolic equation %Z Computer Science [cs]/Other [cs.OH]Reports %X In 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. %G English %2 https://inria.hal.science/inria-00073504/document %2 https://inria.hal.science/inria-00073504/file/RR-3185.pdf %L inria-00073504 %U https://inria.hal.science/inria-00073504 %~ INRIA %~ INRIA-RRRT %~ INRIA-LORRAINE %~ INRIA-NANCY-GRAND-EST %~ TESTALAIN1 %~ INRIA2 %~ LARA