Uniform Energy Decay for Wave Equations with Unbounded Damping Coefficients

• Ikehata Ryo

  Hiroshima University

• Takeda Hiroshi

  Fukuoka Institute of Technology

抄録

We consider the Cauchy problem for wave equations with unbounded damping coefficients in Rⁿ. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence result of a weak solution. In this case we never impose strong assumptions such as compactness of the support of the initial data. This means that we never rely on the finite propagation speed property of the solutions, and we try to deal with an essential unbounded coefficient case. One of our methods comes from an idea developed in [9].

収録刊行物

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 63 (1), 133-152, 2020

  日本数学会函数方程式論分科会

キーワード

• Unbounded damping
• Wave equation
• Cauchy problem
• Weighted initial data
• Multiplier method
• Fourier analysis
• Total energy decay
• Weak solutions

詳細情報

• CRID: 1390566775143638912
• NII論文ID: 130007858187
• DOI: 10.1619/fesi.63.133
• ISSN: 05328721
• Web Site: https://www.jstage.jst.go.jp/article/fesi/63/1/63_133/_pdf
• 本文言語コード: en
• データソース種別:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• 抄録ライセンスフラグ: 使用不可