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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/107199

    Title: On a free boundary problem for the curvature flow with driving force
    Authors: Guo, Jong-Shenq;Matano, Hiroshi;Shimojo, Masahiko;Wu, Chang-Hong
    Date: 2015-05-19
    Issue Date: 2016-08-18 13:34:04 (UTC+8)
    Abstract: We study a free boundary problem associated with the curvature dependent
    motion of planar curves in the upper half plane whose two endpoints slide along the
    horizontal axis with prescribed fixed contact angles. Our first main result concerns
    the classification of solutions; every solution falls into one of the three categories,
    namely, area expanding, area bounded and area shrinking types. We then study in
    detail the asymptotic behavior of solutions in each category. Among other things
    we show that solutions are asymptotically self-similar both in the area expanding
    and the area shrinking cases, while solutions converge to either a stationary solution
    or a traveling wave in the area bounded case. We also prove results on the concavity
    properties of solutions. One of the main tools of this paper is the intersection number
    principle, however in order to deal with solutions with free boundaries, we introduce
    what we call “the extended intersection number principle”, which turns out to be
    exceedingly useful in handling curves with moving endpoints.
    Relation: Archive for Rational Mechanics and Analysis 219, pp.1207-1272
    DOI: 10.1007/s00205-015-0920-8
    Appears in Collections:[Graduate Institute & Department of Mathematics] Proceeding

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