A variational approach to a shape design problem for the wave equation
Arnaud Münch, Pablo Pedregal, Francisco Periago · Comptes Rendus Mathématique · 2006
The problem of determining the optimal damping set for the stabilization of the wave equation may be not well-posed. By means of a vector variational reformulation and use of gradient Young measures, we present a general methodology to relax this kind of problems. From the optimal Young measure associated with the relaxed problem, we obtain information concerning minimizing sequences for the original problem as well as continuity properties of the relaxed cost function.