---
res:
  bibo_abstract:
  - "<jats:title>Abstract</jats:title>\r\n               <jats:p>Maximal parabolic
    $L^p$-regularity of linear parabolic equations on an evolving surface is shown
    by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity
    on a fixed surface. By freezing the coefficients in the parabolic equations at
    a fixed time and utilizing a perturbation argument around the freezed time, it
    is shown that backward difference time discretizations of linear parabolic equations
    on an evolving surface along characteristic trajectories can preserve maximal
    $L^p$-regularity in the discrete setting. The result is applied to prove the stability
    and convergence of time discretizations of nonlinear parabolic equations on an
    evolving surface, with linearly implicit backward differentiation formulae characteristic
    trajectories of the surface, for general locally Lipschitz nonlinearities. The
    discrete maximal $L^p$-regularity is used to prove the boundedness and stability
    of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is
    used to bound the nonlinear terms in the stability analysis. Optimal-order error
    estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm
    is obtained by combining the stability analysis with the consistency estimates.</jats:p>@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Balázs
      foaf_name: Kovács, Balázs
      foaf_surname: Kovács
      foaf_workInfoHomepage: http://www.librecat.org/personId=100441
    orcid: 0000-0001-9872-3474
  - foaf_Person:
      foaf_givenName: Buyang
      foaf_name: Li, Buyang
      foaf_surname: Li
  bibo_doi: 10.1093/imanum/drac033
  dct_date: 2022^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0272-4979
  - http://id.crossref.org/issn/1464-3642
  dct_language: eng
  dct_publisher: Oxford University Press (OUP)@
  dct_subject:
  - Applied Mathematics
  - Computational Mathematics
  - General Mathematics
  dct_title: Maximal regularity of backward difference time discretization for evolving
    surface PDEs and its application to nonlinear problems@
...