Decay property for second order hyperbolic systems of viscoelastic materials

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

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)621-635
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume366
Issue number2
DOIs
Publication statusPublished - 2010 Jun 15
Externally publishedYes

Keywords

  • Decay estimates
  • Energy method
  • Hyperbolic systems
  • Viscoelasticity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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