caa a22 4500 445842148 CHVBK 20180317145347.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00245-011-9148-7 doi (NATIONALLICENCE)springer-10.1007/s00245-011-9148-7 On Shape Optimization for an Evolution Coupled System [Elektronische Daten] [G. Leugering, A. Novotny, G. PerlaMenzala, J. Sokołowski] 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. The Author(s), 2011 Piezoelectricity nationallicence Electromechanical interaction nationallicence Shape sensitivity analysis nationallicence Leugering G. Department of Mathematics, University of Erlangen Nuremberg, Martenstr. 3, 91058, Erlangen, Germany aut Novotny A. Laboratório Nacional de Computação Científica LNCC/MCT, Coordenação de Matemática Aplicada e Computacional, Av. Getúlio Vargas 333, 25651-075, Petrópolis, RJ, Brasil aut PerlaMenzala G. Laboratório Nacional de Computação Científica LNCC/MCT, Coordenação de Matemática Aplicada e Computacional, Av. Getúlio Vargas 333, 25651-075, Petrópolis, RJ, Brasil aut Sokołowski J. Institut Elie Cartan, UMR 7502 (Nancy Université, CNRS, INRIA), Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B.P. 239, 54506, Vandoeuvre-lès-Nancy Cedex, France aut Applied Mathematics & Optimization Springer-Verlag 64/3(2011-12-01), 441-466 0095-4616 64:3<441 2011 64 245 https://doi.org/10.1007/s00245-011-9148-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-011-9148-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Leugering G. Department of Mathematics, University of Erlangen Nuremberg, Martenstr. 3, 91058, Erlangen, Germany aut NATIONALLICENCE 700 1- Novotny A. Laboratório Nacional de Computação Científica LNCC/MCT, Coordenação de Matemática Aplicada e Computacional, Av. Getúlio Vargas 333, 25651-075, Petrópolis, RJ, Brasil aut NATIONALLICENCE 700 1- PerlaMenzala G. Laboratório Nacional de Computação Científica LNCC/MCT, Coordenação de Matemática Aplicada e Computacional, Av. Getúlio Vargas 333, 25651-075, Petrópolis, RJ, Brasil aut NATIONALLICENCE 700 1- Sokołowski J. Institut Elie Cartan, UMR 7502 (Nancy Université, CNRS, INRIA), Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B.P. 239, 54506, Vandoeuvre-lès-Nancy Cedex, France aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 64/3(2011-12-01), 441-466 0095-4616 64:3<441 2011 64 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer