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@ARTICLE{,
            author = {Bathory, Michal and Bul{\'{\i}}{\v c}ek, Miroslav and Sou{\v c}ek, Ondřej},
             title = {Existence and qualitative theory for nonlinear elliptic systems  with a nonlinear interface condition used in electrochemistry},
           journal = {Z. Angew. Math. Phys.},
            volume = {71},
            number = {3},
              year = {2020},
             pages = {Article 74},
               doi = {10.1007/s00033-020-01293-w},
          abstract = {We study a nonlinear elliptic system with prescribed inner interface conditions. These models are frequently used in physical system where the ion transfer plays the important role for example  in modelling of nano-layer growth or Li-on batteries. The key difficulty of the model consists of the rapid or very slow growth of nonlinearity in the constitutive equation inside the domain or on the interface. While on the interface, one can avoid the difficulty by proving a kind of maximum principle of a solution, inside  the domain such regularity for the flux is not available in principle since the constitutive law is discontinuous with respect to the spatial variable. The key result of the paper is the existence theory for these problems, where we require that  the leading functional satisfies either the delta-two or the nabla-two condition. This assumption is applicable in case of fast (exponential) growth as well as in the case of very slow (logarithmically superlinear) growth.},
  Preprint project = {NCMM},
     Preprint year = {2019},
   Preprint number = {06},
       Preprint ID = {NCMM/2019/06}
}