On Shape Optimization for an Evolution Coupled System

Leugering G, Novotny AA, Menzala GP, Sokolowski J (2011)

Publication Type: Journal article

Publication year: 2011


Publisher: Springer Verlag (Germany)

Book Volume: 64

Pages Range: 441--466

Volume: 64

Issue: 3

Journal Issue: 3

DOI: 10.1007/s00245-011-9148-7


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.

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Leugering, G., Novotny, A.A., Menzala, G.P., & Sokolowski, J. (2011). On Shape Optimization for an Evolution Coupled System. Applied Mathematics and Optimization, 64(3), 441--466. https://doi.org/10.1007/s00245-011-9148-7


Leugering, Günter, et al. "On Shape Optimization for an Evolution Coupled System." Applied Mathematics and Optimization 64.3 (2011): 441--466.

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