A new method to obtain uniform decay rates for multidimensional wave equations with nonlinear acoustic boundary conditions

Published

Journal Article

© 2018 Society for Industrial and Applied Mathematics. In this paper, we investigate the uniform stability of a class of nonlinear acoustic wave motions with boundary and localized interior damping. Here the damping and potential in the boundary displacement equation are nonlinear. Moreover, the nonlinear system contains the localized interior damping term, which indicates that there is a thin absorption material and flow resistance on the endophragm of the boundary. Since some lower-order term in the nonlinear wave system is not below the energy level, the “compactness-uniqueness” method is not suitable for the problem. Our main purpose is to present a new method to obtain uniform decay rates for these damped wave equations with nonlinear acoustic boundary conditions.

Full Text

Duke Authors

Cited Authors

  • Gao, Y; Liang, J; Xiao, TJ

Published Date

  • January 1, 2018

Published In

Volume / Issue

  • 56 / 2

Start / End Page

  • 1303 - 1320

International Standard Serial Number (ISSN)

  • 0363-0129

Digital Object Identifier (DOI)

  • 10.1137/16M107863X

Citation Source

  • Scopus