Campuses:

Coffee Break and Poster Session

Tuesday, July 28, 2009 - 10:00am - 11:00am
EE/CS 3-176
  • Global BV for a model of granular flow
    Wen Shen (The Pennsylvania State University)
    Same abstract as the talk.
  • The slow erosion limit in a model of granular flow
    Wen Shen (The Pennsylvania State University)
    Joint work with Debora Amadori
    (Università degli Studi dell'Aquila).

    We study a 2×2 system of balance laws that describes the evolution
    of a granular material (avalanche) flowing downhill. The original
    model was proposed by Hadeler and Kuttler.

    We first consider an initial-boundary value problem, where at the boundary
    the flow of the incoming material is assigned. For this problem we prove
    the global existence of BV solutions for a suitable class of data, with
    bounded by possibly large total variations.

    We then study the slow erosion (or deposition) limit, obtained as the
    thickness of the moving layer tends to zero. We show
    that, in the limit, the profile of the standing layer depends only on the
    total mass of the avalanche flowing downhill, not on the time-law
    describing at which rate the material slides down. More precisely, the
    limiting slope of the mountain profile is provided by an entropy solution
    to a scalar integro-differential conservation law.