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June  2008, 1(2): 243-252. doi: 10.3934/dcdss.2008.1.243

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, United States
2. 

Department of Mathematics, Wayne State University, 656 S Kirby, Detroit, MI 48202, United States

Received  September 2006 Revised  April 2007 Published  March 2008

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.
Keywords: intrinsic shell., nonlinear, Uniqueness, structural acoustic model.
Mathematics Subject Classification: Primary: 35G20, 35A05; Secondary: 74K2.
Citation: Inger Daniels, Catherine Lebiedzik. Existence and uniqueness of a structural acoustic model involving a nonlinear shell. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 243-252. doi: 10.3934/dcdss.2008.1.243
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