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  • Threshold phenomenon for homogenized fronts in random elastic media
    Dondl, Patrick W. ; Jesenko, Martin, 1977-
    We consider a model for the motion of a phase interface in an elastic medium, for example, a twin boundary in martensite. The model is given by a semilinear parabolic equation with a fractional ... Laplacian as regularizing operator, stemming from the interaction of the front with its elastic environment. We show that the presence of randomly distributed, localized obstacles leads to a threshold phenomenon, i.e., stationary solutions exist up to a positive, critical driving force leading to a stick-slip behaviour of the phase boundary. The main result is proved by an explicit construction of a stationary viscosity supersolution to the evolution equation and is based on a percolation result for the obstacle sites. Furthermore, we derive a homogenization result for such fronts in the case of the half-Laplacian in the pinning regime.
    Vir: Discrete and continuous dynamical systems. Series S.. - ISSN 1937-1179 (Vol. 14, iss. 1, 2021, str. 353-372)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2021
    Jezik - angleški
    COBISS.SI-ID - 39638531

    Povezava(-e):

    https://doi.org/10.3934/dcdss.2020329
    DOI

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