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Uniform stabilization of semilinear wave equations with localized internal damping and dynamic Wentzell boundary conditions with a memory term

  • Zhifei Zhang
  • Dandan GuoEmail author
Article
  • 36 Downloads

Abstract

In this paper, we deal with the semilinear wave equations with a local internal damping and dynamic Wentzell boundary conditions with a memory term. The stabilization estimate is more difficult to obtain since the physical energy of the system not only contains the \(H^1\) Sobolev norm of the solution but also depends on the memory term on the boundary. The exponential stabilization is attained by constructing new Lyapunov functionals and using multiplier methods. To illustrate the results, numerical simulations are given in the last part.

Keywords

Uniform stabilization Wave equation on manifold Dynamic Wentzell boundary conditions Memory term Numerical simulations 

Mathematics Subject Classification

35B35 35L70 93D15 

Notes

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and Statistics, Hubei Key Laboratory of Engineering Modeling and Scientific ComputingHuazhong University of Science and TechnologyWuhanChina

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