Decay property for second order hyperbolic systems of viscoelastic materials

Priyanjana M.N. Dharmawardane, Jaime E. Muñoz Rivera, Shuichi Kawashima

研究成果: Contribution to journalArticle査読

29 被引用数 (Scopus)

抄録

We study a class of second order hyperbolic systems with dissipation which describes viscoelastic materials. The considered dissipation is given by the sum of the memory term and the damping term. When the dissipation is effective over the whole system, we show that the solution decays in L2 at the rate t- n / 4 as t → ∞, provided that the corresponding initial data are in L2 ∩ L1, where n is the space dimension. The proof is based on the energy method in the Fourier space. Also, we discuss similar systems with weaker dissipation by introducing the operator (1 - Δ)- θ / 2 with θ > 0 in front of the dissipation terms and observe that the decay structure of these systems is of the regularity-loss type.

本文言語英語
ページ(範囲)621-635
ページ数15
ジャーナルJournal of Mathematical Analysis and Applications
366
2
DOI
出版ステータス出版済み - 6 15 2010

All Science Journal Classification (ASJC) codes

  • 分析
  • 応用数学

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