Global solutions to quasi-linear hyperbolic systems of viscoelasticity

Priyanjana M.N. Dharmawardane, Tohru Nakamura, Shuichi Kawashima

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)

    Abstract

    In the present paper, we study a large-time behavior of solutions to a quasilinear second-order hyperbolic system which describes a motion of viscoelastic materials. The system has dissipative properties consisting of a memory term and a damping term. It is proved that the solution exists globally in time in the Sobolev space, provided that the initial data are sufficiently small. Moreover, we show that the solution converges to zero as time tends to infinity. The crucial point of the proof is to derive uniform a priori estimates of solutions by using an energy method.

    Original languageEnglish
    Pages (from-to)467-483
    Number of pages17
    JournalKyoto Journal of Mathematics
    Volume51
    Issue number2
    DOIs
    Publication statusPublished - Jun 2011

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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