数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 981-994.doi: 10.1016/S0252-9602(15)30032-1

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GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND NONLINEAR BOUNDARY DAMPING-SOURCE INTERACTIONS

吴舜堂   

  1. General Education Center, National Taipei University of Technology, Taipei 106, China
  • 收稿日期:2014-08-19 出版日期:2015-09-01 发布日期:2015-09-01
  • 作者简介:Shun-Tang WU, E-mail: stwu@ntut.edu.tw

GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND NONLINEAR BOUNDARY DAMPING-SOURCE INTERACTIONS

Shun-Tang WU   

  1. General Education Center, National Taipei University of Technology, Taipei 106, China
  • Received:2014-08-19 Online:2015-09-01 Published:2015-09-01

摘要:

A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions imposed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.

关键词: Balakrishnan-Taylor damping, global existence, general decay, relaxation function, viscoelastic equation

Abstract:

A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions imposed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.

Key words: Balakrishnan-Taylor damping, global existence, general decay, relaxation function, viscoelastic equation

中图分类号: 

  • 35L70