Well-posedness of parabolic equations in the non-reflexive and anisotropic Musielak-Orlicz spaces in the class of renormalized solutions. Chlebicka, I., Gwiazda, P., & Zatorska-Goldstein, A. J. Differential Equations, 265(11):5716–5766, 2018.
Well-posedness of parabolic equations in the non-reflexive and anisotropic Musielak-Orlicz spaces in the class of renormalized solutions [link]Paper  doi  bibtex   
@article {MR3857497,
    AUTHOR = {Chlebicka, Iwona and Gwiazda, Piotr and Zatorska-Goldstein,
              Anna},
     TITLE = {Well-posedness of parabolic equations in the non-reflexive and
              anisotropic {M}usielak-{O}rlicz spaces in the class of
              renormalized solutions},
   JOURNAL = {J. Differential Equations},
  FJOURNAL = {Journal of Differential Equations},
    VOLUME = {265},
      YEAR = {2018},
    NUMBER = {11},
     PAGES = {5716--5766},
      ISSN = {0022-0396},
   MRCLASS = {35K59 (35A01 35A02 35B33 35K20)},
  MRNUMBER = {3857497},
MRREVIEWER = {Hongwei Chen},
       DOI = {10.1016/j.jde.2018.07.020},
       URL = {https://doi.org/10.1016/j.jde.2018.07.020},
}

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