, Volume 64, Issue 3, pp 441-466,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 21 Sep 2011

On Shape Optimization for an Evolution Coupled System


A shape optimization problem in three spatial dimensions for an elasto-dynamic piezoelectric body coupled to an acoustic chamber is introduced. Well-posedness of the problem is established and first order necessary optimality conditions are derived in the framework of the boundary variation technique. In particular, the existence of the shape gradient for an integral shape functional is obtained, as well as its regularity, sufficient for applications e.g. in modern loudspeaker technologies. The shape gradients are given by functions supported on the moving boundaries. The paper extends results obtained by the authors in (Math. Methods Appl. Sci. 33(17):2118–2131, 2010) where a similar problem was treated without acoustic coupling.

Author G.L. acknowledges support by the DFG-Cluster of Excellence: Engineering of Advanced Materials (grant).
Author G.P.M acknowledges support by the Brazilian Agency CNPq under grant 301134/2009-0.
Authors A.A.N. and J.S. acknowledge support by the Brazilian-French research programme CAPES/COFECUB under grant 604/08 between LNCC (Petrópolis) and IECN (Nancy).
Author J.S. acknowledge the support of ANR project GAOS.