Shape Optimization Problem for Heat Equation
Antoine Henrot, Jan Sokołowski · 1997
: 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 ! 1 and we prove that it converges to the optimal solution of the stationary problem. The first order necessary optimality conditions are derived. Key-words: shape optimization, Radon measure, shape derivative, parabolic equation (R'esum'e : tsvp) Equipe de Math'ematique, UMR CNRS, Universit'e de Franche-Comt'e, 25030 Besancon Cedex, France; e-mail: [email protected] y Institut Elie Cartan, Laboratoire de Math'ematiques, Universit'e Henri Poincar'e Nancy I, B.P. 239, 54506 Vandoeuvre l`es Nancy Cedex, France and Systems Research Institute of the Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland; e-mail: sokolows@iecn...