---
res:
  bibo_abstract:
  - This paper is concerned with the sharp interface limit for the Allen--Cahn equation
    with a nonlinear Robin boundary condition in a bounded smooth domain Ω⊂\R2. We
    assume that a diffuse interface already has developed and that it is in contact
    with the boundary ∂Ω. The boundary condition is designed in such a way that the
    limit problem is given by the mean curvature flow with constant α-contact angle.
    For α close to 90° we prove a local in time convergence result for well-prepared
    initial data for times when a smooth solution to the limit problem exists. Based
    on the latter we construct a suitable curvilinear coordinate system and carry
    out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear
    Robin boundary condition. Moreover, we show a spectral estimate for the corresponding
    linearized Allen--Cahn operator and with its aid we derive strong norm estimates
    for the difference of the exact and approximate solutions using a Gronwall-type
    argument.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Helmut
      foaf_name: Abels, Helmut
      foaf_surname: Abels
  - foaf_Person:
      foaf_givenName: Maximilian
      foaf_name: Moser, Maximilian
      foaf_surname: Moser
      foaf_workInfoHomepage: http://www.librecat.org/personId=a60047a9-da77-11eb-85b4-c4dc385ebb8c
  bibo_doi: 10.1137/21m1424925
  bibo_issue: '1'
  bibo_volume: 54
  dct_date: 2022^xs_gYear
  dct_identifier:
  - UT:000762768000004
  dct_isPartOf:
  - http://id.crossref.org/issn/0036-1410
  - http://id.crossref.org/issn/1095-7154
  dct_language: eng
  dct_publisher: Society for Industrial and Applied Mathematics@
  dct_subject:
  - Applied Mathematics
  - Computational Mathematics
  - Analysis
  dct_title: Convergence of the Allen--Cahn equation with a nonlinear Robin boundary
    condition to mean curvature flow with contact angle close to 90°@
...