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@ARTICLE{,
            author = {Bul{\'{\i}}{\v c}ek, Miroslav and Glitzky, Annegret and Liero, Matthias},
             title = {Systems describing electrothermal effects with p(x)-Laplacian like structure for discontinuous variable exponents},
           journal = {SIAM J. Math. Anal.,},
            volume = {48},
            number = {5},
              year = {2016},
             pages = {3496--3514},
               doi = {10.1137/16M1062211},
          abstract = {We consider a coupled system of two elliptic PDEs, where the elliptic term in the first equation
shares the properties of the p(x)-Laplacian with discontinuous exponent, while in the second
equation we have to deal with an a priori L1 term on the right hand side. Such a system of equations
is suitable for the description of various electrothermal effects, in particular those, where the
non-Ohmic behavior can change dramatically with respect to the spatial variable, e.g. in organic
light-emitting diodes. We prove the existence of a weak solution under very weak assumptions on
the data and also under general structural assumptions on the constitutive equations of the model.
The main diculty consists in the fact that we have to overcome simultaneously two obstacles -
the discontinuous variable exponent (which limits the use of standard methods) and the L1 right
hand side of the heat equation. Our existence proof based on Galerkin approximation is highly
constructive and therefore seems to be suitable also for numerical purposes.},
  Preprint project = {MORE},
     Preprint year = {2016},
   Preprint number = {02},
       Preprint ID = {MORE/2016/02}
}