% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@ARTICLE{Burger:619107,
      author       = {Burger, Martin and Schuster, Thomas and Wald, Anne},
      title        = {{I}ll-posedness of time-dependent inverse problems in
                      {L}ebesgue-{B}ochner spaces},
      journal      = {Inverse problems},
      volume       = {40},
      number       = {8},
      issn         = {0266-5611},
      address      = {Bristol [u.a.]},
      publisher    = {Inst.},
      reportid     = {PUBDB-2024-07394},
      pages        = {085008},
      year         = {2024},
      abstract     = {We consider time-dependent inverse problems in a
                      mathematical setting using Lebesgue-Bochner spaces. Such
                      problems arise when one aims to recover parameters from
                      given observations where the parameters or the data depend
                      on time. There are various important applications being
                      subject of current research that belong to this class of
                      problems. Typically inverse problems are ill-posed in the
                      sense that already small noise in the data causes tremendous
                      errors in the solution. In this article we present two
                      different concepts of ill-posedness: temporally (pointwise)
                      ill-posedness and uniform ill-posedness with respect to the
                      Lebesgue-Bochner setting. We investigate the two concepts by
                      means of a typical setting consisting of a time-depending
                      observation operator composed by a compact operator.
                      Furthermore we develop regularization methods that are
                      adapted to the respective class of ill-posedness.},
      cin          = {FS-CI},
      ddc          = {004},
      cid          = {I:(DE-H253)FS-CI-20230420},
      pnm          = {623 - Data Management and Analysis (POF4-623) / SFB 1456
                      B06 - Kompensation von Bewegungen und Modellungenauigkeiten
                      in der Nano-CT und lokalen Tomographie (B06) (502871779) /
                      GRK 2756 - GRK 2756: Das Zytoskelett als aktives System –
                      von molekularen Wechselwirkungen zu zellulärer Biophysik
                      (449750155)},
      pid          = {G:(DE-HGF)POF4-623 / G:(GEPRIS)502871779 /
                      G:(GEPRIS)449750155},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001268082400001},
      doi          = {10.1088/1361-6420/ad5a35},
      url          = {https://bib-pubdb1.desy.de/record/619107},
}