Existence and uniqueness of a structural acoustic model involving a nonlinear shell

Inger Daniels; Catherine Lebiedzik

doi:10.3934/dcdss.2008.1.243

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2008, Volume 1, Issue 2: 243-252. Doi: 10.3934/dcdss.2008.1.243

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Existence and uniqueness of a structural acoustic model involving a nonlinear shell

Inger Daniels^1, and
Catherine Lebiedzik^2,

1.
Department of Mathematics, University of Virginia, Kerchoff Hall, Charlottesville, VA 22903
2.
Department of Mathematics, Wayne State University, 656 S Kirby, Detroit, MI 48202

Received: August 31, 2006

Revised: March 31, 2007

Published: May 2008

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Abstract

We consider a structural acoustic model where the active wall is a nonlinear shell. We use a shell modeled with the intrinsic method of Michel Delfour and Jean-Paul Zolésio. We show the existence and uniqueness of solutions in the finite energy space as a consequence of a special trace estimate.

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Mathematics Subject Classification: Primary: 35G20, 35A05; Secondary: 74K25.

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