Stability of Traveling Waves with Degenerate Shock for System of One-Dimensional Viscoelastic Model

K. Nishihara

    Research output: Contribution to journalArticle

    27 Citations (Scopus)

    Abstract

    The stability of traveling wave solutions with shock profile for a system for a one-dimensional viscoelastic material model is investigated. The stress function is not necessarily assumed to be convex or concave, so that the shock condition may be degenerate. Ln some restricted conditions on the stress function it is shown that the traveling wave solution is asymptotically stable, provided the shock is weak and the initial disturbance is small and of integral zero. Proof is given by applying an elementary weighted energy method to the integrated system of the original one. The weight function which is suitably selected plays a key role in the procedure.

    Original languageEnglish
    Pages (from-to)304-318
    Number of pages15
    JournalJournal of Differential Equations
    Volume120
    Issue number2
    DOIs
    Publication statusPublished - 1995 Aug

    Fingerprint

    Viscoelastic Model
    One-dimensional Model
    Traveling Wave
    Shock
    Traveling Wave Solutions
    Viscoelastic Material
    Energy Method
    Integrated System
    Asymptotically Stable
    Weight Function
    Disturbance
    Zero
    Model

    ASJC Scopus subject areas

    • Analysis

    Cite this

    Stability of Traveling Waves with Degenerate Shock for System of One-Dimensional Viscoelastic Model. / Nishihara, K.

    In: Journal of Differential Equations, Vol. 120, No. 2, 08.1995, p. 304-318.

    Research output: Contribution to journalArticle

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