Remarks on the Decay Rate of the Energy for Damped Modified Boussinesq-Beam Equations on the 1-D Half Line

• Charão Ruy Coimbra

  Federal University of Santa Catarina

• Ikehata Ryo

  Hiroshima University

Abstract

We consider the mixed problem for weakly damped modified Boussinesq-Beam equations on the one dimensional half line (0, + ∞). We shall derive fast decay results of the total energy and L²-norm of solutions based on the idea due to [7], which is an essential modification of that developed by Morawetz [15]. In order to apply that idea due to [7] to the one dimensional exterior mixed problem, one also constructs an important Hardy-Sobolev type inequality, which holds only in the 1-D half line case.

Journal

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 60 (2), 239-257, 2017

  Division of Functional Equations, The Mathematical Society of Japan

Keywords

• Damping term
• Modified Boussinesq equation
• Beam equation
• 1-D Half line
• Multiplier method
• Total energy decay
• Weighted initial data

Details

• CRID: 1390001205113055744
• NII Article ID: 130005765969
• DOI: 10.1619/fesi.60.239
• ISSN: 05328721
• Web Site: https://www.jstage.jst.go.jp/article/fesi/60/2/60_239/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed