Implicit Parametrizations and Applications

Abstract : We discuss recent constructive parametrizations approaches for implicit systems, via systems of ordinary differential equations. We also present the notion of generalized solution, in the critical case and indicate some numerical examples in dimension two and three, using MatLab. In shape optimizations problems, using this method, we introduce general optimal control formulations in the boundary observation case. This extends previous work of the authors on optimal design problems with distributed cost functional.