Reduced equations for models of laminated materials in thin domains. I

Article type: Research Article

Authors: DeVille, R.E. Lee^; | Wayne, C. Eugene

Affiliations: Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA E‐mail: [email protected] | Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA

Note: [] Corresponding author.

Abstract: In this paper, we consider a scalar wave equation on a thin, laminated, three‐dimensional plate. We show that if the plate is sufficiently thin, then there is a hierarchy of two‐dimensional equations whose dynamics model the dynamics of the full plate, each of which successively lengthens the time interval over which the approximation holds.

Journal: Asymptotic Analysis, vol. 42, no. 3-4, pp. 263-309, 2005