Decay property for second order hyperbolic systems of viscoelastic materials

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

    Research output: Contribution to journalArticlepeer-review

    33 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 - Jun 15 2010

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Applied Mathematics

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